Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t . Find the following: a E(Y ) b V(Y ) c The

Chapter 3, Problem 3.155

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QUESTION:

Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t . Find the following: a E(Y ) b V(Y ) c The distribution of Y

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QUESTION:

Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t . Find the following: a E(Y ) b V(Y ) c The distribution of Y

ANSWER:

Step 1 of 4

For a discrete random variable , its moment generating function is defined by

From the given moment generating function, the expected value and the variance are calculated using the following relations:

Here,  and  are the first and second derivative of the moment generating function with respect to at.

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