The moment-generating function of a normally distributed random variable, Y , with mean

Chapter 4, Problem 4.139

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QUESTION:

The moment-generating function of a normally distributed random variable, Y , with mean and variance 2 was shown in Exercise 4.138 to be m(t) = et+(1/2)t22 . Use the result in Exercise 4.137 to derive the moment-generating function of X = 3Y + 4. What is the distribution of X? Why?

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QUESTION:

The moment-generating function of a normally distributed random variable, Y , with mean and variance 2 was shown in Exercise 4.138 to be m(t) = et+(1/2)t22 . Use the result in Exercise 4.137 to derive the moment-generating function of X = 3Y + 4. What is the distribution of X? Why?

ANSWER:

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Let  is a normally distributed random variable with mean  and variance  then the moment generating function of  is

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