Question

Qi Suppose X and Y have the following joint PMF. x\y 2 4 8 -1 0 0 1/10 1/5 2/5 0 0 0 1/10 1 1/5 1. Find the marginal P.M.F. for Y, then find E(Y) and Var(Y). 2. Find E(X), the expected value for the absolute value of X. 3. Find the conditional P.M.F. for Y given that \X] = 1, then find E(Y||X| = 1) and Var(Y||X| = 1). 4. Find Cov(X,Y). 5. Are X and Y independent? Explain. 6. Compute Var(X+Y).

Can you just solve 3-6 please?

Answer 1

Solution:

xy 2 Yo 15 | 3/10 2/5 4/0 0 Yo 15 3110 1 El4")= sy ply=4) 8 30.4 = Go /0 4/10 a.) Y 12 ECY)= s y pc yzy) Ply=y) Klo 10 ullo = 2x4+4x2 18x 4,8 :: Var (Y) = 6c427- Ecw]* = 30.4-4.87 2.) P(X) =Ma) he 6110 I 1X1=1) 2 ECVIXI=1) = ux} +9x5 PLY 141=1) 246 % --V141x1=1) 7-36 1X1 - E(1x1) = Co. 3.) = 20/3 4 8 48 EL YIX=1) 3.5556 (4.) ConcX,Y) E(X4) -ECX)ECY) Şeny P(x=x, ) 2 X-IXO + --. 1x8x15 Elxy) - Now, ny (5.) X and Y are independent if P(X=x, Y=y) P(x - 3)/(y-4. for all x,y But it is .. not there in this case X and Y are not independre 6.) var(x +41 '(X) + V(Y) + 2 car(x,y) VIX)= ECX) - ECXD? Elx)=0 PLX =] 360 E(X²) =610.2016 V(X) = 0.6 Now, 0 X L 30

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