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Problem 1E (m.g.f. of Normal random variables). (a) Consider a standard Normal random variable Z N N(0, 1), and compute its m.g.f. wz. Hint: You need
to “complete the square” at the exponent: 5; — tz = %(z2 — 2tz + 132) — £2: = é-(z — t)2 — £23, and then
perform a change of variable in the integral.

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Z ( t ) = e 2 t 2 ... View the full answer

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