Suppose X₁, X2, ..., Xn are i.i.d expoential random variables with parameter A. Let Z = EX₁. Show that Z is the gamma distribution with parameter (A, n) (Hint: By induc- tion, it suffices to check that if X is a gamma distribution with parameter (A, n) and Y is the gamma distribution with parameter (A, n − 1) then X + Y is a gamma distribution with parameter (A, n).)
Suppose X₁, X2, ..., Xn are i.i.d expoential random variables with parameter A. Let Z = EX₁. Show that Z is the gamma distribution with parameter (A, n) (Hint: By induc- tion, it suffices to check that if X is a gamma distribution with parameter (A, n) and Y is the gamma distribution with parameter (A, n − 1) then X + Y is a gamma distribution with parameter (A, n).)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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:Suppose X₁, X2, ..., Xn are i.i.d expoential random variables with parameter A. Let Z =
EX₁. Show that Z is the gamma distribution with parameter (A, n) (Hint: By induc-
tion, it suffices to check that if X is a gamma distribution with parameter (A, n) and Y is
the gamma distribution with parameter (A, n − 1) then X + Y is a gamma distribution with
parameter (A, n).)
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