5.5 Let X1,.., Xn be iid with pdf fx(r), and let X denote the sample mean. Show that .... fx (1) = nfx1+ +…+Xn (nx), even if the mgf of X does not exist.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5.5 Let X1,..., Xn be iid with pdf fx(r), and let X denote the sample mean. Show that
fx (x) = nfx,+.+X, (nz),
1+……
even if the mgf of X does not exist.
Transcribed Image Text:5.5 Let X1,..., Xn be iid with pdf fx(r), and let X denote the sample mean. Show that fx (x) = nfx,+.+X, (nz), 1+…… even if the mgf of X does not exist.
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