Let X be an exponential random variable with parameter and moment generating fun

Question

Let X be an exponential random variable with parameter and moment generating function mX(t) = /( – t). Let random variable Y = 2X. Then the moment generating function of Y is

mY(t) = /( – 2t)

mY(t) = /(2 – t)

mY(t) = /( – t)2

mY(t) = 2/( – t)

Let X be an exponential random variable with parameter and moment generating function mX(t) = /( – t). Let random variable Y = 2X. Then the moment generating function of Y is

A.

mY(t) = /( – 2t)

B. None of the given mgf’s. C.

mY(t) = /(2 – t)

D.

mY(t) = /( – t)2

E.

mY(t) = 2/( – t)

Explanation / Answer

If X and Y have same distirbution then mX(t)=mY(t) in that situation the answer is (A).

Otherwise if answer (E) is correct

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