MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Suppose that Z1, Z2, . . . , Zn are statistically independent random variables. Define Y as the sum of squares of these random variables

n
Y => Z² (n ≥ 2)
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 Z², 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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Transcribed Image Text:n Y => Z² (n ≥ 2) 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 Z², 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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