Suppose Xi ~ Poisson(λi ), i=1,2,3, and that the X1's are independent. Let Y1=X1+X2 , Y2 = X2 + X3 a. Find the joint MG

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answerhappygod
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Suppose Xi ~ Poisson(λi ), i=1,2,3, and that the X1's are independent. Let Y1=X1+X2 , Y2 = X2 + X3 a. Find the joint MG

Post by answerhappygod »

Suppose Xi ~ Poisson(λi ),
i=1,2,3, and that the X1's are independent.
Let Y1=X1+X2 ,
Y2 = X2 + X3

a. Find the joint MGF of Y1 and
Y2 (mY1mY2(t1,t2))

b. Find Cov(Y1,Y2) using the joint MGF from
a.
c. Find Cov(Y1,Y2) using properties of
expectations
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