If x~n(3, 4, y~n(-2, 6, z~n(1, 3, and x and y and z are independent, what are the distribution, expectation and variance of s = 3x-2y z?

I assume refers to a random variable following a ormal distribution with mean and variance .

Recall that the moment generating function for a random variable is



and that the moment generating function for a linear combination of random variables is equivalent to the product of each individual random variables moment generating functions; that is, if , then



So you have



with





which means



This is the moment generating function of yet another normal distribution, so that , with expectation 14 and variance 63.

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