Use moment generating functions to decide whether or not the given random variables X and Y...

Use moment generating functions to decide whether or not the given random variables X and Y are equal in distribution.

a). The random variables Z1, Z2, Z3 are independent normal N(0,1), X = Z1 + Z2 + Z3 and Y = √3Z1

b). The random variables Z1, Z2, Z3 are independent Poisson with the same parameterλ, X = 3Z1 and Y=Z1 + Z2 + Z3

c). The random variables Z1, Z2 are independent normal N(0,1), X = Z1 + 2Z2 and Y= 2Z1 − Z2.

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orchestra answered 1 year ago

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