2. (20 points) A Poisson random variable X with parameter l = 1 is used to form the random variable Y = aX + b with a = 3 and b = 1. (a) Find the moment generating function for Y. (b) Use the moment generating function from part (a) to find the mean of Y, µY and the variance of Y, s2 Y. Note that whilte there are other ways of finding these values, you will only receive credit for using the moment generating function.

image 47 - 2. (20 points) A Poisson random variable X with parameter l = 1 is used to form the random variable Y = aX + b with a = 3 and b = 1. (a) Find the moment generating function for Y. (b) Use the moment generating function from part (a) to find the mean of Y, µY and the variance of Y, s2 Y.  Note that whilte there are other ways of finding these values, you will only receive credit for using the moment generating function.

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images - 2. (20 points) A Poisson random variable X with parameter l = 1 is used to form the random variable Y = aX + b with a = 3 and b = 1. (a) Find the moment generating function for Y. (b) Use the moment generating function from part (a) to find the mean of Y, µY and the variance of Y, s2 Y.  Note that whilte there are other ways of finding these values, you will only receive credit for using the moment generating function.

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