概率伦与款醒统外「 性质2(x分布的数学期望和方差) 若x2~X2(n,则E(x2)=n,D(x2)=2n. 证明 因为X,~N(0,1),所以E(X;)=D(X)=1, D(X;)=E(X;)-[E(X;)23-2=1,i=1,2,n. 放Ex)=42x2Ex=n ()(x)=2n. 性质2 ~ ( ), ( ) , ( ) 2 . 2 2 2 2 若   n 则 E  = n D  = n 证明 X ~ N(0, 1), 因为 i ( ) ( ) 1, 2 所以 E Xi = D Xi = 2 4 2 2 ( ) ( ) [ ( )] D Xi = E Xi − E Xi = 3 − 2 = 1, i = 1, 2,  , n.       = = n i E E Xi 1 2 2 故 ( ) = = n i E Xi 1 2 ( ) = n,       = = n i D D Xi 1 2 2 ( ) = = n i D Xi 1 2 ( ) = 2n. ( )  2分布的数学期望和方差