diff --git a/stdlib/random.pyi b/stdlib/random.pyi
index 74201216ba58..b031ade0b608 100644
--- a/stdlib/random.pyi
+++ b/stdlib/random.pyi
@@ -103,9 +103,14 @@ class Random(_random.Random):
     def betavariate(self, alpha: float, beta: float) -> float: ...
     def expovariate(self, lambd: float) -> float: ...
     def gammavariate(self, alpha: float, beta: float) -> float: ...
-    def gauss(self, mu: float, sigma: float) -> float: ...
+    if sys.version_info >= (3, 11):
+        def gauss(self, mu: float = ..., sigma: float = ...) -> float: ...
+        def normalvariate(self, mu: float = ..., sigma: float = ...) -> float: ...
+    else:
+        def gauss(self, mu: float, sigma: float) -> float: ...
+        def normalvariate(self, mu: float, sigma: float) -> float: ...
+
     def lognormvariate(self, mu: float, sigma: float) -> float: ...
-    def normalvariate(self, mu: float, sigma: float) -> float: ...
     def vonmisesvariate(self, mu: float, kappa: float) -> float: ...
     def paretovariate(self, alpha: float) -> float: ...
     def weibullvariate(self, alpha: float, beta: float) -> float: ...
@@ -154,9 +159,16 @@ def triangular(low: float = ..., high: float = ..., mode: float | None = ...) ->
 def betavariate(alpha: float, beta: float) -> float: ...
 def expovariate(lambd: float) -> float: ...
 def gammavariate(alpha: float, beta: float) -> float: ...
-def gauss(mu: float, sigma: float) -> float: ...
+
+if sys.version_info >= (3, 11):
+    def gauss(mu: float = ..., sigma: float = ...) -> float: ...
+    def normalvariate(mu: float = ..., sigma: float = ...) -> float: ...
+
+else:
+    def gauss(mu: float, sigma: float) -> float: ...
+    def normalvariate(mu: float, sigma: float) -> float: ...
+
 def lognormvariate(mu: float, sigma: float) -> float: ...
-def normalvariate(mu: float, sigma: float) -> float: ...
 def vonmisesvariate(mu: float, kappa: float) -> float: ...
 def paretovariate(alpha: float) -> float: ...
 def weibullvariate(alpha: float, beta: float) -> float: ...