a. Find E(Y^{2}), E(X^{2})

b. Find σ^{2 }x σ^{2 }y c. Find P(X=1|Y=1), P(X=2|Y=2) (for this one I got 1/4 on both, I'm stuck on a and b). Much help is appreciated!

Probability for (X∩Y)

y=1 y=2

x=1 1/4 1/8 3/8

x=2 3/8 1/4 5/8

5/8 3/8 1

E(y) =5/8*1 +3/8 *2 = 11/8

E(X) = 3/8*1+5/8*2 =13/8

a)

E ( y^{2 }) = 5/8*1^{2}+3/8* 2^{2} = 17/8

E ( x^{2 }) = 3/8*1^{2}+5/8* 2^{2} = 23/8

b)

Sigma_{x}^{2} = E ( x^{2}) –[E(x)]^{2} = 23/8 -169/64 = 184/64-169/64 = 15/64

Sigma_{y}^{2} = E ( y^{2}) –[E(y)]^{2} = 17/8 -121/64 = 136/64-121/64 = 15/64

c)

P( x=1 | y=1 ) = 1/ 4 /(5/8) = 2/8*(8/5)=2/5

P( x=2 | y=2 ) = 1/ 4 /(3/8) = 2/8*(8/3)=2/3

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