Random Vari X, Y both discrete and take values of 1 or 2. Probability for (X∩Y)

Statistics
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a. Find E(Y2), E(X2

 b. Find  σ2 x σy 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!

y=1y=2
x=11/41/8
x=23/81/4

Feb 19th, 2015

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 ( y2 ) = 5/8*12+3/8* 22 = 17/8

E ( x2 ) = 3/8*12+5/8* 22 = 23/8

b)

Sigmax2 = E ( x2) –[E(x)]2 = 23/8 -169/64 = 184/64-169/64 = 15/64

Sigmay2 = E ( y2) –[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


Feb 19th, 2015

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