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The moment-generating function of a normally distributed random variable, Y , with mean
Chapter 4, Problem 4.139(choose chapter or problem)
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?
Questions & Answers
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:Step 1 of 3
Let is a normally distributed random variable with mean and variance then the moment generating function of is