Question 3 Suppose that Z₁, Z2,..., Zn are statistically independent. random variables. Define Y as the sum of squares of these random variables: 4 n Y = Z² (n ≥ 2) -[4 i=1 (a) Express the moment generating function My (t) of the random variable Y in terms of moment generating functions involving the random variables Z?, i = 1,..., n. (b) Determine My(t) for the special case that Z; ~ N(0, 1). (c) For the above special case, calculate E[Y] by using the moment generating function.

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