answer.tex

\chapter*{习题答案}
\addcontentsline{toc}{chapter}{习题答案}

\setcounter{chapter}{1}
\setcounter{section}{0}
\begin{answer}
  \item \begin{enumerate}
    \item $\Omega= \{(0,0,0),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,0,1),
        (1,1,0),(1,1,1)\}$，其中0表示反面，1表示正面.
    \item $\Omega=\{(x,y,z):x,y,z=1,2,3,4,5,6\}$.
    \item $\Omega=\{(1),(0,1),(0,0,1),(0,0,0,1),\cdots\}$.
    \item $\Omega=\{0,1,2,\cdots\}$.
    \item $\Omega=\{t:t\ge0\}$.
  \end{enumerate}

  \item $A=\{(0,0,0),(0,1,0),(1,0,0),(0,1,1),(1,0,1),(1,1,0),(1,1,1)\}$，

    $B=\{(0,0,0),(0,0,1),(0,1,0),(1,0,0)\}$，

    $C=\{(0,0,1),(0,1,0),(1,0,0)\}$，

    $D=\{(0,0,0),(1,1,1)\}$.

  \item \begin{enumerate*}
    \item $ABC\cup \bar A\bar B\bar C$.
    \item $A\bar B\bar C\cup \bar AB\bar C\bar A\bar BC$.
    \item $\bar{ABC}=\bar A\cup \bar B\cup C$.
    \item $AB\cup AC\cup BC$.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item $A\supset B$.
    \item $A\supset B$.
  \end{enumerate*}

  \item \begin{enumerate}
    \item $\bar AB=\{x|0.25\le x\le0.5\}\cup\{x|1<x<1.5\}$.
    \item $\bar A\cup B=\Omega=\{x|0\le x\le2\}$.
    \item $\bar{AB}=\bar A=\{x|0\le x\le0.5\}\cup\{x|1<x\le2\}$.
    \item $\bar{A\cup B}=\bar B=\{x|0\le x<0.25\}\cup\{x|1.5\le x\le2\}$.
  \end{enumerate}

  \item $A=\{X=1\},B=\{X\ge1\},C=\{X=2\},D=\{X=0\}$.

  互不相容的事件为：$A$与$C$，$A$与$D$，$B$与$D$，$C$与$D$. 对立的事件为：$B$与$D$.

  \item 成立的为(2)，不成立的为(1) (3) (4).
  \item 不能.
  \item \begin{enumerate*}
    \item $\bar A=$“掷二次硬币，至少有一反面”.
    \item $\bar B=$“设计三次，至少一次不命中目标”.
    \item $\bar C=$“加工四个零件，全部为不合格品”.
  \end{enumerate*}
\end{answer}

\begin{answer}
  \stepcounter{enumi}
  \item $3/4$.
  \item $1/2$.
  \item \begin{enumerate*}
    \item $1/6$.
    \item $5/18$.
    \item $1/6$.
  \end{enumerate*}
  \item $p=19/36,q=1/18$.
  \item \begin{enumerate}
    \item 0.0026
    \item 0.0106
    \item 0.1055
    \item 0.1104
  \end{enumerate}
  \item 0.3，0.6，0.1.
  \item $13/28$.
  \item $19/40$.
  \item $\frac{\mathrm C_{k-1}^1\mathrm C_{n-k}^1}{\mathrm C_n^2}$.
  \item \begin{enumerate*}
    \item $8/15$.
    \item $1/20$.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item $\frac{5^3}{6^3}$.
    \item $\frac{5^3-4^3}{6^3}$.
  \end{enumerate*}

  \item $1/15$.

  \item $\frac2{n-1}$.

  \item $\frac{\mathrm P_{10}^5}{10^5}$.

  \item $8/15$.

  \item $\frac{n+1}{\mathrm C_{2n}^n}$.

  \item $\frac2{\mathrm C_{2n}^n}$.

  \item $\frac{\mathrm C_{n+1}^m}{\mathrm C_{n+m}^m}$.

  \item $3/8,9/16,1/16$.

  \item 0.212.

  \item \begin{enumerate}
    \item $\frac{\binom{N+n-k-2}{n-k}}{\binom{N+n-1}n},\;0\le k\le n$.
    \item $\frac{\binom Nm\binom{n-1}{N-m-1}}{\binom{N+n-1}n},\;N-n\le m\le N-1$.
    \item $\frac{\binom{m+j-1}{m-1}\binom{N-m+n-j-1}{n-j}}
    {\binom{N+n-1}n},1\le m\le N,0\le j\le n$.
  \end{enumerate}

  \item $17/25$.
  \item 0.879.
  \item $\frac{a+b+c}{d\pi}$.
  \item 0.866.
  \item $5/9$.
  \item 0.5966.
\end{answer}

\begin{answer}
  \item \begin{enumerate*}
    \item (c).
    \item (d).
    \item (a).
    \item (b).
    \item (e).
  \end{enumerate*}

  \item (4)(6)是正确的.

  \item $2/7$.

  \item \begin{enumerate*}
    \item $7/15$.
    \item $14/15$.
    \item $7/30$.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item 0.30.
    \item 0.73.
    \item 0.90.
    \item 0.10.
  \end{enumerate*}

  \item $1-\frac{\mathrm C_7^3}{\mathrm C_{11}^3}$.

  \item $p_1=0.5177,p_2=0.4914$.

  \item $1-\frac{8^n+5^n-4^n}{9^n}$.

  \item $1-\frac{(n-1)^{k-1}}{n^k}$.

  \item 0.5.
  \item 0.5.
  \item \begin{enumerate*}
    \item $1/16$.
    \item $3/8$.
  \end{enumerate*}

  \item 0.7772.
  \item $1-\frac1{2!}+\frac1{3!}+\cdots+(-1)^{n-1}\frac1{n!}$.
  \item \begin{enumerate*}
    \item $P(AB)=P(A)$时，$P(AB)$达到最大值0.6.
    \item $P(A\cup B)=1$时，$P(AB)$达到最小值0.3.
  \end{enumerate*}

  \item $1-p$.
  \item 0.6.
\end{answer}

\begin{answer}
  \item \begin{enumerate*}
    \item 0.2
    \item 0.6
  \end{enumerate*}

  \item $2/3$.

  \item $P(A|B)=1/15,P(B|A)=1/3$.

  \item 0.5.

  \item 0.2.

  \item $\frac{m-1}{2n-m-1}$.

  \item $P(B|A)=1/3,P(A|B)=1/15$.

  \item $1/3$.

  \item 0.25.

  \item $7/12$.

  \item \begin{enumerate*}
    \item $\frac1{n+1}$.
    \item $\frac1{n(n+1)}$.
  \end{enumerate*}

  \item $3/5$.

  \item \begin{enumerate*}
    \item $\frac{a(n+1)+bn}{(a+b)(n+m+1)}$.
    \item $\frac{a(a-1)(n+2)+2ab(n+1)+b(b-1)n}{(a+b)(a+b-1)(n+m+2)}$.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item 0.96.
    \item 0.5
  \end{enumerate*}

  \item 0.9524.

  \item 0.43.

  \stepcounter{enumi}

  \item \begin{enumerate*}
    \item 0.4.
    \item 0.4856.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item 0.8.
    \item 0.5.
  \end{enumerate*}

  \item $2/3$.

  \item $\frac1{(2n-1)!!}$.

  \item $\frac1{m-1}\left(1-\frac1{(m-1)^{n-2}}\right),n=2,3,\cdots$.

  \item $\frac12\left[1+\left(\frac23\right)^{n-1}\right],
  n=2,3,\cdots$.

  \item $\frac12\left[1+\left(\frac13\right)^n\right],
  n=1,2,\cdots$.

  \item $\frac12[1+(2p-1)^{n-1}],n=2,3,\cdots$.
\end{answer}


\begin{answer}
  \item $3/5$.

  \item \begin{enumerate*}
    \item 0.56.
    \item 0.94.
    \item 0.38.
  \end{enumerate*}

  \item $15/22$.

  \item \begin{enumerate*}
    \item 0.552.
    \item 0.012.
    \item 0.328.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item 0.003.
    \item 0.388.
    \item 0.059.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item $26/27$.
    \item $2/9$.
    \item $7/27$.
  \end{enumerate*}

  \item 0.

  \item \begin{enumerate*}
    \item 0.3.
    \item 0.5.
    \item 0.7
  \end{enumerate*}

  \item \begin{enumerate*}
    \item 0.5.
    \item 0.025.
  \end{enumerate*}

  \item $P(A)=P(B)=0.5$.

  \item $11/24$.

  \item 0.375.

  \item $2/3$.

  \item 11.

  \item 0.66.

  \item $\frac{(\lambda p)^r}{r!}\ee^{-\lambda p}$.

  \item \begin{enumerate*}
    \item 0.0507.
    \item 0.0341.
  \end{enumerate*}

  \item 五局三胜制对甲更有利.

  \item 甲得冠军的概率$5/14$，乙得冠军的概率$5/14$，丙得冠军的概率$2/7$.

  \item \begin{enumerate}
    \item 甲得全部赌本的$1/2$，乙得全部赌本的$1/2$.
    \item 甲得全部赌本的$11/16$，乙得全部赌本的$5/16$.
    \item 记$a=\mathrm C_{n+m-1}^0+\mathrm C_{n+m-1}^1+\cdots+
    \mathrm C_{n+m-1}^{m-1},b=\mathrm C_{n+m-1}^m+\mathrm C_{n+m-1}^{m-1}+\cdots+\mathrm C_{n+m-1}^{n+m-1}$，则甲得全部赌本的$a/2^{n+m-1}$，乙得全部赌本的$b/2^{n+m-1}$.
  \end{enumerate}
\end{answer}

\stepcounter{chapter}

\begin{answer}
  \item \begin{enumerate}
    \item $\begin{array}{c|ccc}
      X & 3 & 4 & 5 \\
      \midrule
      P & 0.1 & 0.3 & 0.6
    \end{array}$
    \item $F(x)=\begin{cases}
      0, & x<3, \\
      0.1, & 3\le x<4,\\
      0.4, & 4\le x<5, \\
      1, & 5\le x.
    \end{cases}$
  \end{enumerate}

  \item \begin{enumerate}
    \item $\begin{array}{c|cccccc}
      X & 1 & 2 & 3 & 4 & 5 & 6 \\
      \midrule
      P & 11/36 & 9/36 & 7/36 & 5/36 & 3/36 & 1/36
    \end{array}$
  \item $F(x)=\begin{cases}
    0, & x<1, \\
    11/36, & 1\le x<2, \\
    20/36, & 2\le x<3, \\
    27/36, & 3\le x<4, \\
    32/36, & 4\le x<5, \\
    35/36, & 5\le x<6, \\
    1, & 6\le x.
  \end{cases}$
  \end{enumerate}

  \item \begin{enumerate}
    \item $\begin{array}{c|cccc}
      X & 1 & 2 & 3 & 4 \\
      \midrule
      P & 7/10 & 7/30 & 7/120 & 1/120
    \end{array}$
    \item $\begin{array}{c|cccc}
      X & 1 & 2 & 3 & 4 \\
      \midrule
      P & 7/10 & 6/25 & 27/500 & 3/500
    \end{array}$
  \end{enumerate}

  \item \begin{enumerate}
    \item $\begin{array}{c|cccc}
      X & 0 & 1 & 2 & 3 \\
      \midrule
      P & 5/30 & 15/30 & 9/30 & 1/30
    \end{array}$
    \item $1/3$.
  \end{enumerate}

  \item \begin{enumerate}
    \item $P(X=k)=\frac{\mathrm C_{90}^{5-k}\mathrm C_{10}^k}{\mathrm C_{100}^5},k=0,1,2,3,4,5$.
    \item 0.4162.
  \end{enumerate}

  \item $\begin{array}{c|cccc}
    X & 0 & 1 & 3 & 6 \\
    \midrule
    P & 1/4 & 1/12 & 1/6 & 1/2
  \end{array}$.\quad $1/3,1/2,2/3,3/4$.

  \item $\ln2,1,\ln1.25$.

  \item $1-\alpha-\beta$.

  \item \begin{enumerate*}
    \item $F(x)=\begin{cases}
      0, & x<2, \\
      3/10, & 2\le x<3, \\
      7/10, & 3\le x <4, \\
      1, & 4\le x.
    \end{cases}$
    \item 0,0.
  \end{enumerate*}

  \item $F(x)=\begin{cases}
    0, & x<-1 \\
    x^2/2+x+1/2, & -1\le x<0, \\
    -x^2/2+x+1/2, & 0\le x<1, \\
    1, & 1\le x.
  \end{cases}$

  \item 0.875.

  \item \begin{enumerate*}
    \item $A=1/2$.
    \item $\sqrt2/4$.
  \end{enumerate*}

  \item \begin{enumerate*}
    \item $A=1$.
    \item 0.4.
    \item $p(x)=2x,0<x<1$.
  \end{enumerate*}

  \item \begin{enumerate}
    \item $c=21$.
    \item $F(x)=\begin{cases}
      0, & x<0, \\
      7x^3+\frac12x^2, & 0\le x<0.5, \\
      1, & 0.5\le x.
    \end{cases}$
    \item $17/54$.
    \item $103/108$.
    \item $\sqrt[3]{4}$.
  \end{enumerate}
\end{answer}

\begin{answer}
  \item $E(X)=-0.2,E(3X+5)=4.4$.
  \item 1.9.
  \item 1.201.
  \item $\begin{array}{c|cccccc}
    X & 0 & 1 & 2 & 3 & 4 & 5\\
    \midrule
    P & 0.0511 & 0.2554 & 0.3973 & 0.2384 & 0.0542 & 0.0036
  \end{array},E(X)=2$.
  \item 乙组砝码.
  \item $2/9$.
  \item $\frac{1-(1-p)^4}p$.
  \item 50.
  \item 0.2.
  \item 7.
  \item 1.
  \item \begin{enumerate*}
    \item 11.
    \item 100.
    \item 20.
  \end{enumerate*}
  \item 5.
  \item $3/4$.
\end{answer}

\begin{answer}
  \item 1.
  \item 0.2173.
  \item 9.
  \item 6.5.
  \item 1.5.
  \setcounter{enumi}{10}
  \item $8/9$.
\end{answer}

\begin{answer}
  \item 0.0972.
  \item 0.9933.
  \item 0.784.
  \item 0.0001279.
  \item $n=6,p=0.4$.
  \item $89/81$.
  \item \begin{enumerate*}
    \item 0.1905.
    \item 0.1912.
  \end{enumerate*}
  \item 0.0902.
  \stepcounter{enumi}
  \item $n/m$.
  \item 1.
  \item $9/64$.
  \item 1.0556.
\end{answer}

\begin{answer}
  \item $20/27$.
  \item $3/4$.
  \item $4/5$.
  \item $602/3$.
  \item $\frac{\pi(a^2+b^2+ab)}{12}$.
  \item 21.
  \item 0.4712.
  \item 0.1523.
  \item 4.
  \item 33.6402.
  \item 0.5167.
  \item $1-\ee^{-1}$.
  \item $k=\ln2/\lambda$.
  \item $[1,3]$.
  \item $-2,1/\sqrt2;0,1/2;0,1/\sqrt2$.
  \item 0.595.
  \item \begin{enumerate*}
    \item $\mu=70,\sigma=14.81$.
    \item 0.94.
  \end{enumerate*}
  \item 0.0456.
  \item 0.6826.
  \item \begin{enumerate*}
    \item 0.5328.
    \item 0.6977.
    \item 3.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item 0.9544.
    \item 0.63.
    \item $d\le0.16$.
  \end{enumerate*}
  \item 0.8698.
  \item \begin{enumerate*}
    \item 0.1587.
    \item 0.6915.
    \item 0.6826.
  \end{enumerate*}

  \item 79.
  \item $a=55.36,b=58.5,c=61.5,d=64.44$.
  \item 一样大小.
  \item 0.95.
  \item 不变.
  \item 24.3
  \item $\sigma\sqrt{2/\pi}$.
  \item 由上题可得.
  \item 0.5940.
  \item 0.2639，0.1818.
  \item 0.4096.
\end{answer}

\begin{answer}
  \item $\begin{array}{c|cccc}
    Y & 0 & 1 & 4 & 9 \\
    \midrule
    P & \frac15 & \frac7{30} & \frac15 & \frac11{30}
  \end{array},
  \begin{array}{c|cccc}
    Z & 0 & 1 & 2 & 3 \\
    \midrule
    P & \frac15 & \frac7{30} & \frac15 & \frac11{30}
  \end{array}$
  \item $\begin{array}{c|cc}
    Y & -1 & 1 \\
    \midrule
    P & 0.5 & 0.5
  \end{array}$.
  \item $\begin{array}{c|cc}
    Y & -1 & 1 \\
    \midrule
    P & 1/3 & 1/3
  \end{array}$.
  \item $1-X\sim U(0,1)$.
  \item $p(y)=\frac2{\pi\sqrt{1-y^2}},0<y<1$.
  \item $p(y)=\frac1{\sqrt{\pi y}},0<y<\pi/4$.
  \item $p(y)=\frac1{2y},\ee^2<y<\ee^4$.
  \item \begin{enumerate*}
    \item $p(y)=\frac1{4\sqrt y},0<y<4$.
    \item $\frac1{\sqrt2}$.
  \end{enumerate*}
  \item $p(y)=1/15,2<y<17$.
  \item \begin{enumerate}
    \item $p(y)=0.5\ee^{-0.5y},y>0$.
    \item $p(y)=1/3,1<y<4$.
    \item $p(y)=1/y,1<y<\ee$.
    \item $p(y)=\ee^{-y},y>0$.
  \end{enumerate}
  \item \begin{enumerate*}
    \item $p(y)=y^2/18,-3<y<3$.
    \item $p(y)=3(3-y)^2/2,2<y<4$.
    \item $p(y)=3\sqrt y/2,0<y<1$.
  \end{enumerate*}
  \item $p(y)=\frac1{\sqrt{2\pi y}\sigma}\ee^{-\frac y{2\sigma^2}},y>0$.
  \item $p(y)=\frac1{\sqrt{2\pi}y\sigma}\ee^{-
  \frac{(\ln y-\mu)^2}{2\sigma^2}},y>0.E(Y)=\ee^{\mu+\frac{\sigma^2}2},
  \Var(Y)=\ee^{2\mu+\sigma^2}(\ee^{\sigma^2}-1)$.
  \item \begin{enumerate}
    \item $p(y)=\sqrt{\frac2\pi}\ee^{-\frac{y^2}2},y>0$.
    \item $p(y)=\frac1{2\sqrt{\pi(y-1)}}\ee^{-\frac{y-1}4},y>1$.
  \end{enumerate}
  \item \begin{enumerate}
    \item $p(y)=\frac12\ee^{-\frac{y-1}2},y>1$.
    \item $p(y)=\frac1{y^2},y>1$.
    \item $p(y)=\frac1{2\sqrt y}\ee^{-\sqrt y},y>0$.
  \end{enumerate}
  \setcounter{enumi}{17}
  \item 0.9772.
\end{answer}

\begin{answer}
  \item $\mu_1=(a+b)/2,\mu_2=(a^2+ab+b^2)/3,\mu_3=(a^3+a^2b+ab^2+b^3)/4
      .\nu_1=0,\nu_2=(b-a)^2/12,\nu_3=0,\nu_4=(b-a)^4/80,\beta_1
      =0,\beta_2=-1.2$.
  \item $\sqrt3/3$.
  \item $\mu_1=\alpha/\lambda,\mu_2=\alpha(\alpha+1)/\lambda^2,
      \mu_3=\alpha(\alpha+1)(\alpha+2)/\lambda^3,\nu_1=0,\nu_2
      =\alpha/\lambda^2,\nu_3=2\alpha/\lambda^3$.
  \item $\mu_1=1/\lambda,\mu_2=2/\lambda^2,\mu_3
      =6/\lambda^3,\mu_4=24/\lambda^4.\nu_1=0,\nu_2=1/\lambda^2,
      \nu_3=2\alpha/\lambda^3,\nu_4=9/\lambda^4.C_v(X)=1,\beta_1=2,
      \beta_2=6$.
  \item $x_{0.1}=6.16,x_{0.9}=13.84$.
  \item $x_{0.5}=\ee^{\mu}$.
  \item $x_p=\eta[-\ln(1-p)]^{1/m}$；当$m=1.5,\eta=1000$时，$x_{0.1}=
      223.08,x_{0.5}=783.22,x_{0.8}=1373.36$.
  \item $x_{0.1}=0.211,x_{0.5}=1.386,x_{0.8}=3.219$.
\end{answer}

\stepcounter{chapter}
\begin{answer}
  \item $p_{ij}=\frac{5!}{i!j!(5-i-j)!}0.5^i0.3^j0.2^{0.5-i-j,i+j\le5}$.
  \item $p_{ij}=\frac{\binom{50}i\binom{30}j\binom{20}{5-i-j}}
  {\binom{100}5},i+j\le5$.
  \item $9/35$.
  \item 0.
  \item \begin{enumerate*}
    \item $1/8$.
    \item $3/8$.
    \item $27/32$.
    \item $2/3$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item 12.
    \item $F(x,y)=(1-\ee^{-3x})(1-\ee^{-4y}),x>0,y>0$.
    \item $1-\ee^{-3}-\ee^{-8}+\ee^{-11}$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item $15/64$.
    \item 0.
    \item 0.5.
    \item $F(x)=\begin{cases}
      0, & x<0\,\text{或}\, y<0, \\
      x^2y^2, & 0\le x<0, 0\le y<1,\\
      x^2, & 0\le x<1,1\le y,\\
      y^2, & 1\le x,0\le y<1, \\
      1, & x\ge1,y\ge1.
    \end{cases}$
  \end{enumerate*}
  \item \begin{enumerate*}
    \item 6.
    \item $1/12,0.6642$.
  \end{enumerate*}
  \item \begin{enumerate}
    \item $1/8$.
    \item $7/8,1/2$.
    \item $3/4$.
  \end{enumerate}
  \item $\begin{array}{c|cc}
    X_1\backslash X_2 & 0 & 1 \\
    \midrule
    0 & 1-\ee^{-1} & 0 \\
    1 & \ee^{-1}-\ee^{-2} & \ee^{-2}
  \end{array}$.
  \item $65/72$.
  \item 0.5809.
  \item $5/8$.
  \item 0.044.
\end{answer}

\begin{answer}
  \item $\begin{array}{c|ccc}
    X & -1 & 0 & 1 \\
    \midrule
    P & 5/12 & 1/6 & 5/12
  \end{array},
  \begin{array}{c|ccc}
    Y & 0 & 1 & 2 \\
    \midrule
    P & 7/12 & 1/3 & 1/12
  \end{array}$
  \item $F_X(x)=1-\ee^{-\lambda_1x},x>0.\quad
  F_Y(y)=1-\ee^{-\lambda_2y},y>0$.
  \item $p_X(x)=2\sqrt{1-x^2}/\pi,-1<x<1.\quad
  p_Y(y)=2\sqrt{1-y^2}/\pi,-1<y<1$.
  \item $p(x,y)=2,1<x<\ee^2,0<y<1/x.\quad p_X(x)=2/x,1<x<\ee^2$.
  \item \begin{enumerate}
    \item $p_X(x)=\ee^{-x},x>0.\quad p_Y(y)=y\ee^{-y},y>0$.
    \item $p_X(x)=5(1-x^4)/8,-1<x<1.\quad
    p_Y(y)=5\sqrt{1-y}(1+2y)/6,0<y<1$.
  \end{enumerate}
  \item $p_X(x)=6(x-x^2),0<x<1.\quad p_Y(y)=6(\sqrt y-y),0<y<1$.
      \stepcounter{enumi}
  \item 0.5.
  \item 0.89.
  \item $a=1/18,b=2/9,c=1/6$.
  \item $p=17/36,q=1/18$.
  \item \begin{enumerate}
    \item $p(x,y)=\ee^{-y},0<x<1,y>0$.
    \item $\ee^{-1}$.
    \item $\ee^{-1}$.
  \end{enumerate}
  \item \begin{enumerate}
    \item $p_X(x)=3x^2,0<x<1.\quad p(x,y)=3(1-y^2)/2,0<y<1$.
    \item 不独立.
  \end{enumerate}
  \item \begin{enumerate}
    \item $p_X(x)=\begin{cases}
      1+x, & -1<x<0, \\
      1-x, & 0<x<1, \\
      0, & \text{其他},
    \end{cases}\;p_Y(y)=\begin{cases}
      2y, & 0<y<1, \\
      0, & \text{其他}.
    \end{cases}$
    \item 不独立.
  \end{enumerate}
  \item $2/9$.
\end{answer}

\begin{answer}
  \item $\begin{array}{c|ccc}
    U & 1 & 2 & 3 \\
    \midrule
    P & 0.12 & 0.37 & 0.51
  \end{array},
  \begin{array}{c|ccc}
    V & 0 & 1 & 2 \\
    \midrule
    P & 0.40 & 0.44 & 0.16
  \end{array}$
  \item $P(Z=1)=\lambda/(\lambda+\mu),\quad P(Z=0)=\mu/(\lambda+\mu)$.
  \item $\begin{array}{c|cc}
    Z & 0 & 1 \\
    \midrule
    P & 0.25 & 0.75
  \end{array}$
  \item \begin{enumerate}
    \item $\begin{array}{c|cc}
      Z & 0 & 1 \\
      \midrule
      P & 0.25 & 0.75
    \end{array}$
    \item $(1-p)^{i-1}p[2-(1-p)^{i-1}-(1-p)^i],i=1,2,\cdots$.
  \end{enumerate}
    \item $5/7$.
    \item \begin{enumerate}
      \item $p_Z(z)=4z\ee^{-2z},z>0$.
      \item $p_Z(z)=\ee^{-|z|}/2,-\infty<z<+\infty$.
    \end{enumerate}
    \item $p_Z(z)=3(1-z^2)/2,0<z<1$.
    \item \begin{enumerate}
      \item $p_2(x)=x^3\ee^{-x}/6,x>0$.
      \item $p_3(x)=x^5\ee^{-x}/120,x>0$.
    \end{enumerate}
    \item \begin{enumerate}
      \item $p_Z(z)=\begin{cases}
        z, & 0\le z<1, \\
        2-z, & 1\le z<2, \\
        0, & \text{其他}.
      \end{cases}$
      \item $p_Z(z)=\begin{cases}
        1-\ee^{-z}, & 0<z<1, \\
        (\ee-1)\ee^{-z}, & z>1, \\
        0, & \text{其他}.
      \end{cases}$
    \end{enumerate}
    \item $p_Z(z)=(\ln2-\ln z)/2,0<z<2$.
    \item $\begin{array}{c|ccc}
      X & -1 & 0 & 1 \\
      \midrule
      P & 0.1344 & 0.7312 & 0.1344
    \end{array}$
    \item $p_T(t)=3\lambda\ee^{-3\lambda t},t>0$.
    \item $p_Z(z)=z\ee^{-z^2/2},z>0$.
    \item \begin{enumerate}
      \item $p(u,v)=u\ee^{-u},u>0,0<v<1$.
      \item 独立.
    \end{enumerate}
\end{answer}

\begin{answer}
  \item $91/36$.
  \item $E(X)=7n/2,\Var(X)=35n/12$.
  \item $(n+2)/3$.
  \item $(n-1)/(n+1)$.
  \item $(2n-1)/(n-1)$.
  \item 0.25.
  \item $4/3,1/18$.
  \item $5/8$.
  \item $p_Y(y)=10y^9,0<y<1;E(Y)=10/11;\Var(Y)=5/726$.
  \stepcounter{enumi}
  \item \begin{enumerate}
    \item $1/n\lambda$.
    \item $n/\lambda-\mathrm C_n^2(1/2\lambda)+\mathrm C_n^3
    (1/3\lambda)+\cdots+(-1)^{n-1}(1/n\lambda)$.
  \end{enumerate}
  \item \begin{enumerate*}
    \item $1/2\lambda$.
    \item $3/2\lambda$.
  \end{enumerate*}
  \item $1/\sqrt\pi$.
  \item $E(Y)=n\theta/(n+1),E(Z)=\theta/(n+1)$.
  \item 2.
  \item 14166.67.
  \item $-0.02$.
  \item $-n/36,-1/5$.
  \item $-2/3$.
  \item $-n/4,-1$.
  \item $3/5$.
  \item $1,1$.
  \item 0.25.
  \item $2/3,0,0$.
  \item $3/\sqrt{57}$.
  \item $\rho$.
  \item 0.5692.
  \item $(a^2-b^2)/(a^2+b^2)$.
  \item \begin{enumerate*}
    \item $\sqrt{(1-\rho)/\pi}$.
    \item 0,0.
  \end{enumerate*}
  \item $1/36,1/2$.
  \item $-\frac1{147},-\frac{\sqrt5}{23}$.
  \item $\frac1{\sqrt3}$.
  \item \begin{enumerate}
    \item $\begin{pmatrix}
      1/18 & 0 \\
      0 & 3/80
    \end{pmatrix}$.
    \item $\begin{pmatrix}
      11/36 & -1/36 \\
      -1/36 & 11/36
    \end{pmatrix}$.
  \end{enumerate}
  \item $a=0.5$时，$X$与$Y$不相关.
  \item 当$d\ne0$时，$\rho_{12}=\rho_{13}=\rho_{23}=1$. 当$d=0$时，$\rho_{12}=(c^2-a^2-b^2)/2ab,\rho_{13}=(b^2-a^2-c^2)/2ac,\rho_{23}
      =(a^2-b^2-c^2)/2bc$.
\end{answer}

\begin{answer}
  \item $\frac{n!}{m!(n-m)!}\left(\frac{7.14}{14}\right)^m
  \left(\frac{6.86}{14}\right)^{n-m},m=0,1,\cdots,n$.
  \item 当$0<x<1$时，$p(y|x)=1/x,0<y<x$.
  \item 当$-1<y<1$时，$p(x|y)=1/(1-|y|),|y|<x<1$.
  \item $7/15$.
  \item $47/64$.
  \item $E(X|Y=2)=78/25,E(Y|X=0)=2$.
  \item $n\lambda_1/(\lambda_1+\lambda_2)$.
  \item $7/12$.
  \item $(2y+1)/3$.
  \item $(\lambda+9)/(2\lambda)$.
\end{answer}

\stepcounter{chapter}

\begin{answer}
  \item $0.4+0.3\ee^{\ii t}+0.2\ee^{2\ii t}+0.1\ee^{3\ii t}$.
  \item $\varphi(t)=\frac{p\ee^{\ii t}}{1-q\ee^{\ii t}},E(X)=\frac1p,\Var(X)=\frac q{p^2}$.
  \item $\left( \frac{p\ee^{\ii t}}{1-q\ee^{\ii t}} \right)^r$.
  \item \begin{enumerate*}
    \item $\frac{a^2}{a^2+t^2}$.
    \item $\ee^{-a|t|}$.
  \end{enumerate*}
  \item $0,3a^4$.
  \setcounter{enumi}{12}
  \item $\ee^{\ii\mu t-\frac{\sigma^2t^2}{2n}}$.
\end{answer}

\begin{answer}
  \item 验证马尔可夫条件.
  \item 验证马尔可夫条件.
  \item 验证马尔可夫条件.
  \item 验证马尔可夫条件.
  \item 验证马尔可夫条件.
  \item 不适用.
  \item 由辛钦大数定律知$\{X_n\}$服从大数定律.
  \item 由辛钦大数定律知$\{X_n\}$服从大数定律.
  \item 是.
\end{answer}

\begin{answer}
  \setcounter{enumi}{5}
  \item (1)(3)不是，(2)是.
\end{answer}

\begin{answer}
  \item \begin{enumerate*}
    \item $b(100,0.2)$.
    \item 0.9437.
  \end{enumerate*}
  \item 0.9155.
  \item 0.0062.
  \item 0.9966.
  \item 0.9836.
  \item 0.8665.
  \item \begin{enumerate*}
    \item 24000元.
    \item 0.90.
  \end{enumerate*}
  \item 0.0071.
  \item \begin{enumerate*}
    \item 0.1802.
    \item 443.
  \end{enumerate*}
  \item 0.0787.
  \item 0.0254.
  \stepcounter{enumi}
  \item \begin{enumerate*}
    \item 0.8185.
    \item 81.
  \end{enumerate*}
  \item 9488.
  \item 842.
  \item 16.
  \item 12655.
  \item 104.
  \item 66307.
\end{answer}

\stepcounter{chapter}
\setcounter{section}{2}

\begin{answer}
  \item $\bar x=3,s^2=3.7778,s=1.9437$.
  \setcounter{enumi}{2}
  \item $\bar y=3\bar x-4,s_y^2=9s_x^2$.
  \setcounter{enumi}{5}
  \item $\bar y_B=a\bar x_A+b,s_B^2=a^2s_A^2,R_B=aR_A,m_B=am_A+b$.
  \setcounter{enumi}{7}
  \item $E(\bar x)=0,\Var(\bar x)=\frac1{3n}$.
  \setcounter{enumi}{9}
  \item $n\ge250$，利用中心极限定理可得$n\ge68$.
  \item $\bar x\overset{\cdot}{\sim}N\left(\frac1\lambda,
      \frac1{40\lambda^2}\right)$.
  \item $\bar x\overset{\cdot}{\sim}N\left(\frac52,\frac1{12}\right)$.
  \item $\bar x\overset{\cdot}{\sim}N\left(p,\frac{p(1-p)}{20}\right)$.
  \item $\sqrt{\frac98}(\approx1.0607)$.
  \item 12.8571.
  \item $163,9.2338,0.1829,-0.9618$.
  \item 0.046875.
  \item
    \begin{gather*}
      \begin{array}{c|ccccc}
        x_{(1)} & 1 & 2 & 3 & 4 & 5 \\
        \midrule
        p & 369\times \left(\frac15\right)^4 & 175\times \left(\frac15\right)^4 & 65 \times \left(\frac15\right)^4 & 15 \times \left(\frac15\right)^4 & \left(\frac15\right)^4
      \end{array}\\
      \begin{array}{c|ccccc}
        x_{(4)} & 1 & 2 & 3 & 4 & 5 \\
        \midrule
        p & \left(\frac15\right)^4 & 15\times \left(\frac15\right)^4 & 65 \times \left(\frac15\right)^4 & 175 \times \left(\frac15\right)^4 & 369 \times \left(\frac15\right)^4
      \end{array}
    \end{gather*}
    \item \begin{enumerate*}
      \item 0.9370.
      \item 0.3308.
    \end{enumerate*}
    \item $x_{(5)}\sim f(y)=\frac{9!}{4!4!}(3y^2-2y^3)^4\cdot 6y(1-y)\cdot(1-3y^2+2y^3)^4,0<y<1$.
\end{answer}

\begin{answer}
  \item $n\ge3$.
  \item $n\ge97$.
  \item 0.3859.
  \item 0.8983（用软件计算）.
  \item 0.6329（用软件计算）.
  \item $\frac{u_{\alpha}}{\sqrt n}$.
  \setcounter{enumi}{7}
  \item $Y\sim F(m,n)$.
  \item $Y\sim F(1,1)$.
  \item 0.9938（用软件计算）.
  \setcounter{enumi}{11}
  \item $\frac1{\sqrt{1+\frac1n}}$，自由度为$n-1$.
  \item 0.0978（用软件计算）.
\end{answer}

\begin{answer}
  \setcounter{enumi}{4}
  \item $\prod_{i=1}^nx_i$.
  \item $\sum_{i=1}^nx_i^m$.
  \item $\prod_{i=1}^nx_i$.
  \item $\sum_{i=1}^n|x_i|$.
  \item \begin{enumerate*}
    \item $\sum_{i=1}^n(x_i-\mu)^2$.
    \item $\sum_{i=1}^nx_i$.
  \end{enumerate*}
  \item $(x_{(1)},x_{(n)})$.
  \item $(x_{(1)},x_{(n)})$.
\end{answer}

\stepcounter{chapter}
\begin{answer}
  \item 1143.7500，96.0562.
  \item 2.2680.
  \item \begin{enumerate*}
    \item $2\bar x+1$.
    \item $\frac2{\bar x}$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item $3\bar x$.
    \item $\frac{2\bar x-1}{1-\bar x}$.
    \item $\left( \frac{\bar x}{1-\bar x} \right)^2$.
    \item $\hat\mu_M=\bar x-\sqrt{\bar{x^2}-(\bar x)^2},
    \hat\theta_M=\sqrt{\bar{x^2}-(\bar x)^2}$.
  \end{enumerate*}
  \item $\varPhi^{-1}\left(\frac kn\right)$.
  \item \begin{enumerate*}
    \item $\frac{ab}c$.
    \item $\frac{ab}c-a-b+c$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item $\left(\frac n{\sum_{i=1}^n\ln x_i}\right)^2$.
    \item $\max\left( \frac n{\sum_{i=1}^n\ln x_i-n\ln c},1 \right)$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item $x_{(1)}$.
    \item $\hat\theta_{\text{MLE}}=x_{(1)}$.
    \item $\frac{x_{(n)}}{k+1}$.
  \end{enumerate*}
  \item \begin{enumerate}
    \item $\frac{\sum_{i=1}^n|x_i|}n$.
    \item $\hat\theta_{\text{MLE}}$可取$(x_{(n)}-0.5,x_{(1)}+0.5)$中任意值.
    \item $\hat\theta_{1\text{MLE}}=x_{(1)},
    \hat\theta_{2\text{MLE}}=x_{(n)}$.
  \end{enumerate}
  \item 0.4990.
  \item $\frac{2(\bar x-1)}{\bar x}$.
  \item 28.3058.
\end{answer}

\begin{answer}
  \item \begin{enumerate}
    \stepcounter{enumii}
    \item $\frac{x_{(n)}}2$，不是无偏估计，是相合估计.
  \end{enumerate}
  \item $\hat \mu_3$.
  \setcounter{enumi}{3}
  \item $\frac1{2(n-1)}$.
  \setcounter{enumi}{5}
  \item $a=\frac{n_1-1}{n_1+n_2-2},b=\frac{n_2-1}{n_1+n_2-2}$.
  \item $a_i=\frac{\frac1{\sigma_i^2}}{\sum_{i=1}^n\frac1{\sigma_i^2}},
      i=1,\cdots,k$.
  \item \begin{enumerate}
    \stepcounter{enumii}
    \item 当$1\le n\le7$时，$\hat\theta_1$比$\hat\theta_2,\hat\theta_3$更有效；当$n\ge8$时，$\hat\theta_2,\hat\theta_3$都比$\hat\theta_1$更有效（$\hat\theta_2,\hat\theta_3$两者的效率相等）.
  \end{enumerate}
  \item \begin{enumerate}
    \item $\bar x-\bar y$.
    \item $n_1=\frac n3,n_2=\frac{2n}3$.
  \end{enumerate}
  \item 两者效率相等.
  \item $\bar{x^2}-\bar x$.
  \item 当$n=1,2$时，两者效率相等；当$n\ge3$时，$\frac12(x_{(1)}+x_{(n)})$更有效.
  \item \begin{enumerate}
    \item $\hat\sigma_1^2$.
    \item 当$n=1$时，三者均方误差相等；当$n\ge2$时，$\hat\sigma_3^2$的均方误差最小.
  \end{enumerate}
  \item \begin{enumerate}
    \item $x_{(1)}$，是相合估计，不是无偏估计.
    \item $\bar x-1$，是相合估计，是无偏估计.
    \item $\frac1n,MSE(\hat\theta_1)-MSE(\hat\theta_{\frac1n})
    =\frac2{n62}-\frac1{n^2}=\frac1{n^2},MSE(\hat\theta_2)-
    MSE(\hat\theta_{\frac1n})=\frac1n-\frac1{n^2}=\frac{n-1}{n^2}$.
  \end{enumerate}
\end{answer}

\begin{answer}
  \setcounter{enumi}{5}
  \item \begin{enumerate*}
    \item $-\frac{\sum_{i=1}^n\ln x_i}n$.
    \item $-\frac{\sum_{i=1}^n\ln x_i}n$.
  \end{enumerate*}
  \item $\frac n{\theta^2}$.
  \item $\frac{2n}{\theta^2(1-\theta)}$.
\end{answer}

\begin{answer}
  \item $P(\lambda=1.5|x=3)=0.3899,P(\lambda=1.6|x=3)
  =0.6101$.
  \item $U(10.7,16)$.
  \item \begin{enumerate*}
    \item $Be\left(n=1,\sum_{i=1}^nx_i+1\right)$.
    \item 0.25.
  \end{enumerate*}
  \setcounter{enumi}{5}
  \item \begin{enumerate}
    \item $p\big(\theta|(x_1,\cdots,x_n)\big)=
    \begin{cases}
      \frac{2n-1}{\theta^{2n}[x_{(n)}^{-2n+1}-1]}, & x_{(n)}<\theta<1 , \\
      0, & \text{其他}.
    \end{cases}$
    \item $p\big(\theta|(x_1,\cdots,x_n)\big)=
    \begin{cases}
      \frac{2n-3}{\theta^{2n}[x_{(n)}^{-2n+3}-1]}, & x_{(n)}<\theta<1 , \\
      0, & \text{其他}.
    \end{cases}$
  \end{enumerate}
  \item $\frac{\alpha+n}{\lambda-\sum_{i=1}^n\ln x_i}$.
  \item \begin{enumerate*}
    \stepcounter{enumii}
    \item $\frac{(\beta+n)\cdot\max(x_{(n)},\theta_0)}{\beta+n-1}$.
  \end{enumerate*}
  \item $Ga(0.0004,2)$.
\end{answer}

\begin{answer}
  \item $[1.9168,2.5832]$.
  \item $n\ge\left(\frac{3.92\sigma}k\right)^2$.
  \item \begin{enumerate*}
    \item $[-0.9800,0.9800]$.
    \item $[0.6188,4.3929]$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item $[0.1486,0.4215]$.
    \item $[56.0739,56.5661]$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item $[432.3064,482.6936]$.
    \item $[438.9058,476.0942]$.
    \item $[24.2239,64.2935]$.
  \end{enumerate*}
  \item $[0.07416,0.2008]$.
  \setcounter{enumi}{7}
  \item $[11.0001,12.9583]$.
  \item \begin{enumerate*}
    \item $[-0.0939,12.0939]$.
    \item $[-0.2063,12.2063]$.
    \item $[-0.2154,12.2154]$.
    \item $[0.3359,4.0973]$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item $[0.06203,1.0075]$.
    \item $[-0.4060,0.4460]$.
  \end{enumerate*}
\end{answer}

\stepcounter{chapter}
\begin{answer}
  \item \begin{enumerate*}
    \item 0.0036，0.0368.
    \item 34.
  \end{enumerate*}
  \item 0.0328\quad 0.6331.
  \item $c=0.98,0.8299$.
  \item $(2.5/3)^n,17$.
\end{answer}

\begin{answer}
  \item 拒绝，这批枪弹的初速有显著降低.
  \item 接收，可认为现在生产之铁水平均含碳量仍为4.55.
  \item 拒绝，平均重量不是15 g.
  \item 接收，这一天包装机的工作正常.
  \item $n\ge7$.
  \item \begin{enumerate*}
    \item 接收.
    \item 接收.
  \end{enumerate*}
  \item 可以.
  \item 校长的看法是对的.
  \item 不能.
  \item 接收.
  \item 拒绝.
  \item 能.
  \item 可以.
  \item 有显著差别.
  \item 检验统计量：$U=\frac{\bar x-2\bar y}{\sqrt{\frac{\sigma_1^2}n+\frac{4\sigma_2^2}m}}$，拒绝域为：$\{U>u_{1-\alpha}\}$.
  \item 正常.
  \item 无显著差异.
  \item 显著偏大.
  \item 没有显著差异.
  \item 接收.
  \item \begin{enumerate*}
    \item 接收.
    \item 接收.
  \end{enumerate*}
  \item 不能.
\end{answer}

\begin{answer}
  \item 不能.
  \item 有明显提高.
  \item 接收，0.2969.
  \item 有，0.0314.
  \item 不能，0.0179.
  \item 不能，0.0047.
\end{answer}

\begin{answer}
  \item 能.
  \item 能.
  \item 能.
  \item 能.
  \item 能.
  \item 不独立.
  \item 不可以.
  \item 不可以.
  \item 不可以.
  \item 接收.
  \item 接收.
\end{answer}

\stepcounter{chapter}
\begin{answer}
  \item $S_e=42.75,f_e=9;S_A=105.5,f_A=2;S_T=148.25,f_A=11$.
  \item $f_e=20.5,\hat\sigma^2=2.5625$.
  \item $S_e=20.5,\hat\sigma^2=2.5625$.
  \item
  \begin{tabularx}{0.7\linewidth}{ZZZZZ}
    \toprule
    来源 & 平方和 & 自由度 & 均方和 & $F$比 \\
    \midrule
    因子$A$ & 4.2 & 2 & 2.1 & 7.5 \\
    误差$e$ & 2.5 & 9 & 0.28 \\
    \midrule
    和$T$ & 6.7 & 11 \\
    \bottomrule
  \end{tabularx}

  显著.
  \item 显著.
  \item 显著.
  \item \begin{enumerate*}
    \item 有显著影响.
    \item $(7.16,8.81),(5.57,7.23),(8.29,9.95)$.
  \end{enumerate*}
  \item \begin{enumerate*}
    \item 显著.
    \item 第五组，$(24,99,30,99)$.
  \end{enumerate*}
\end{answer}

\begin{answer}
  \item 水平1、3之间无显著差异，它们与水平2有显著差异.
  \item 水平5与水平1，3，4之间以及水平2水平4之间有显著差异，其他无显萧差异.
  \item 不显著，$(6.34,6.96)$.
  \item
  \begin{tabularx}{0.7\linewidth}{ZZZZZ}
    \toprule
    来源 & 平方和 & 自由度 & 均方和 & $F$比 \\
    \midrule
    因子$A$ & 20.125 & 2 & 10.063 & 15.72 \\
    误差$e$ & 15.362 & 24 & 0.640 \\
    \midrule
    和$T$ & 35.487 &26 \\
    \bottomrule
  \end{tabularx}

  显著，水平2、3之间无显著差异，它们与水平1有显著差异.
\end{answer}

\begin{answer}
    \item 接收.
    \item 接收.
    \item 接收.
    \item 接收.
    \item 接收.
    \item 接收.
\end{answer}

\begin{answer}
  \item \begin{enumerate}
    \item $\hat\beta=\frac{\sum_{i=1}^nx_iy_i}{\sum_{i=1}^nx_i^2}
      ,\hat{\sigma^2}=\frac1{n-1}\sum_{i=1}^n(y_i-\hat\beta x_i)^2$.
    \item $\frac{\sigma^2}{\sum_{i=1}^nx_i^2}$.
    \end{enumerate}
    \item 一致.
    \setcounter{enumi}{3}
    \item 一般不重合，有交点，$(\bar x,\bar y)$.
    \item \begin{enumerate*}
      \setcounter{enumii}{1}
      \item 0.9597.
      \item $\hat y =22.6486+0.2643x$.
      \item 显著.
    \end{enumerate*}
    \item $3,0811,(7.8695,8.1520)$.
    \item \begin{enumerate}
      \item $\hat y =35.2389+84.3975x$.
      \item $\hat\beta_1\sim N(\beta_1,3.3069\sigma^2),
      \hat\beta_0\sim n(\beta_0,0.1142\sigma^2)$.
      \item $-0.6726$.
      \item 显著
      \begin{center}
      \begin{tabularx}{0.7\linewidth}{ZZZZZ}
        \toprule
        来源 & 平方和 & 自由度 & 均方和 & $F$比 \\
        \midrule
        回归 & 2154.0239 & 1 & 2154.0239 & 108.29 \\
        误差 & 278.4805 & 14 & 19.8915 \\
        \midrule
        和 & 2432.4566 & 15 \\
        \bottomrule
      \end{tabularx}
      \end{center}
      \item $(79.1372,89.6575)$.
      \item $(38.0288,57.7682)$.
    \end{enumerate}
    \item \begin{enumerate}
      \item $\hat\beta_1=1.591,\hat\beta_0=24.2991$.
      \item 显著.
      \item $(25.1553,26.9439)$.
    \end{enumerate}
    \item \begin{enumerate}
      \item 显著.
      \begin{center}
      \begin{tabularx}{0.7\linewidth}{ZZZZZ}
        \toprule
        来源 & 平方和 & 自由度 & 均方和 & $F$比 \\
        \midrule
        回归 & 0.0810 & 1 & 0.0810 & 55.7339 \\
        误差 & 0.0436 & 30 & 0.01453 \\
        \midrule
        和 & 0.1246 & 31 \\
        \bottomrule
      \end{tabularx}
      \end{center}
      \item 0.8063.
      \item $(1.4500,1.5994)$.
    \end{enumerate}
    \item \begin{enumerate}
      \setcounter{enumi}{1}
      \item $\hat y=-2.26+0.0487x$，显著.
      \begin{center}
      \begin{tabularx}{0.7\linewidth}{ZZZZZ}
        \toprule
        来源 & 平方和 & 自由度 & 均方和 & $F$比 \\
        \midrule
        回归 & 203.40 & 1 & 203.40 & 179.65 \\
        误差 & 7.93 & 7 & 1.13 \\
        \midrule
        和 & 211.33 & 8 \\
        \bottomrule
      \end{tabularx}
      \end{center}
      \item $(9.688,14.999)$.
      \item $\hat y=0.0417x$，显著.
    \end{enumerate}
\end{answer}

\begin{answer}
  \item $u=\ln x,v=y$.
  \item $u=\sqrt x,v=y$.
  \item $u=x,v=\ln(y-100),\beta_0=\ln a,\beta_1=-1/b$.
  \item 不能.
  \item 能.
  \item 能.
  \item $\hat y=1053.633\ee^{-0.247x},R^2=0.9902,s=96.1417$.
\end{answer}