Suppose Y1, Y2, Y3, and Y4 are mutually independent and identically distributed exponential random variables with mean 1. a) Find the moment generating function of the sum T = Yı+Y2+Y3+Y4. What is the distribution of T? b) Find the pdf of the maximum order statistic Y(4).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
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Suppose Y1, Y2, Y3, and Y4 are mutually independent and identically distributed exponential
random variables with mean 1.
a) Find the moment generating function of the sum T = Yı+Y2+Y3+Y4. What is the distribution
of T?
b) Find the pdf of the maximum order statistic Y(4).
Transcribed Image Text:Suppose Y1, Y2, Y3, and Y4 are mutually independent and identically distributed exponential random variables with mean 1. a) Find the moment generating function of the sum T = Yı+Y2+Y3+Y4. What is the distribution of T? b) Find the pdf of the maximum order statistic Y(4).
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