46. For a standard normal random variable Z, let n = E[Z]. Show that n = (2/)!...

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46. For a standard normal random variable Z, let µn = E[Z"]. Show that

µn =

(2/)!

2/j!

when n is odd

(2/)!

2j/j!

when n = 2j HINT: Start by expanding the moment generating function of Z into a Taylor series about 0 to obtain E[e^z] = e^(1/2)τ²

= ∑ (τ²)^j / j!

j=0

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A First Course In Probability

ISBN: 9780137463145

5th Edition

Authors: Sheldon M. Ross

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Question Posted: Sep 14, 2024 05:01 AM

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46. For a standard normal random variable Z, let n = E[Z"]. Show that n = (2/)! 2/j! when n is odd (2/)! 2j/j! when n = 2j HINT: Start by expanding the moment generating function of Z into a Taylor...
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46. For a standard normal random variable Z, let n = E[Z]. Show that n = (2/)!...

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A First Course In Probability

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