Let Z ~ N(0, 1). z? ? a. What is the probability density function of X = b. Let Z1, Z2, Z - N(0, 1) be k independent standard normal random variables. What is the probability density function of Y = Z+ ...+ Z?
Let Z ~ N(0, 1). z? ? a. What is the probability density function of X = b. Let Z1, Z2, Z - N(0, 1) be k independent standard normal random variables. What is the probability density function of Y = Z+ ...+ Z?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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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Transcribed Image Text:Let Z ~ N(0, 1).
a. What is the probability density function of X = Z? ?
b. Let Z1, Z2, · · ·
Z - N(0, 1) be k independent standard normal random variables.
What is the probability density function of Y
Z + ...+ Z ?
(Hint: Compute T(1/2) by an adequate change of variables, then recognize the distribution
of Z computed in the first question.)
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