Joint distribution for random variables X and Y are shown be

Joint distribution for random variables X and Y are shown below

Joint distribution for random variables X and Y are shown below Are X and Y independent (show why or why not)? Find E(XY).

Solution

they will be indepdent only if P(X;Y ) = P(x) * P(Y)

P(X) =

for 1      0.15

for 2       0.40

for 3       0.45

P(Y)

for 3       0.45

for 5       0.55

P(1,3 ) = 0.10

lets see with P(1) * P(3) that the result of this multiplication is 0.15 * 0.45 =0.0675

so they are dependents

b)

1*3*0.10 + 0.20*3*2 + 3*4*0.15 + 5*1*0.05 + 0.20*2*5 + 0.30 * 5 * 3

0.3 + 1.2 + 1.8 + 0.25 + 2 + 4.5

10.05