diff --git a/core/kernel.rbs b/core/kernel.rbs
index 619f4ecd1..23f808641 100644
--- a/core/kernel.rbs
+++ b/core/kernel.rbs
@@ -1318,10 +1318,10 @@ module Kernel : BasicObject
   #
   # See also Random.rand.
   #
-  def self?.rand: () -> Float
-                | (Integer arg0) -> Integer
-                | (::Range[Integer] arg0) -> Integer
-                | (::Range[Float] arg0) -> Float
+  def self?.rand: (?0) -> Float
+                | (int arg0) -> (Integer | Float)
+                | (::Range[Integer] arg0) -> Integer?
+                | (::Range[Float] arg0) -> Float?
 
   # <!--
   #   rdoc-file=io.c
diff --git a/test/stdlib/Kernel_test.rb b/test/stdlib/Kernel_test.rb
index 53d4027f8..bfb29ad5d 100644
--- a/test/stdlib/Kernel_test.rb
+++ b/test/stdlib/Kernel_test.rb
@@ -95,6 +95,19 @@ def test_autoload?
                        Kernel, :autoload?, interned
     end
   end
+
+  def test_rand
+    assert_send_type "() -> Float", Kernel, :rand
+    assert_send_type "(0) -> Float", Kernel, :rand, 0
+    assert_send_type "(_ToInt) -> Float", Kernel, :rand, 0.0
+    assert_send_type "(_ToInt) -> Float", Kernel, :rand, 0r
+    assert_send_type "(_ToInt) -> Float", Kernel, :rand, 0i
+    assert_send_type "(_ToInt) -> Integer", Kernel, :rand, 10
+    assert_send_type "(Range[Integer]) -> Integer", Kernel, :rand, 1..10
+    assert_send_type "(Range[Integer]) -> nil", Kernel, :rand, 0...0
+    assert_send_type "(Range[Float]) -> Float", Kernel, :rand, 0.0...10.0
+    assert_send_type "(Range[Float]) -> nil", Kernel, :rand, 0.0...0.0
+  end
 end
 
 class KernelTest < StdlibTest