Question 3 Suppose that Z₁, Z2,..., Zn are statistically independent random variables. Define Y as the sum of squares of these random variables: (L) Y = w w for th i=1 (a) Express the moment generating function My (t) of the random variable Y in tern of moment generating functions involving the random variables Z, i = 1,..., n. Z² (n ≥ 2) 72 NO 1

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Question 3
Suppose that Z₁, Z2, ..., Zn are statistically independent
random variables. Define Y as the sum of squares of these random variables:
Y =
n
i=1
Z² (n ≥2)
(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 Z₁ ~ N(0, 1).
Transcribed Image Text:Question 3 Suppose that Z₁, Z2, ..., Zn are statistically independent random variables. Define Y as the sum of squares of these random variables: Y = n i=1 Z² (n ≥2) (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 Z₁ ~ N(0, 1).
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