Suppose X and Y are two independent random variables such that EX^(4)=2, EY^(2)=1, EX^(2)=1, and EY=0. Compute Var(X^(2)Y)

Josiah Owens 2022-10-23 Answered
Suppose X and Y are two independent random variables such that E X 4 = 2 , E Y 2 = 1 , E X 2 = 1, and EY = 0. Compute V a r ( X 2 Y )
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Answers (1)

bargeolonakc
Answered 2022-10-24 Author has 16 answers
V a r ( X 2 Y ) = E ( X 4 Y 2 ) E ( X 2 Y ) 2 = E ( X 4 ) E ( Y 2 ) E ( X 2 ) 2 E ( Y ) 2 = 2 × 1 1 × 0 = 2
(The expectations can be split as X and Y are independent, and hence X 2 is independent of Y and X 4 is independent of Y 2 )
Result:
2
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