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N Y =X; i=1 exponentially distributed with parameter Xp using conditioning arguments directly with the random sum, instead using the m.g.f. method. nt: Write the C.D.F of the Gamma random variable in terms of the Poisson process.

N Y =X; i=1 exponentially distributed with parameter Xp using conditioning arguments directly with the random sum, instead using the m.g.f. method. nt: Write the C.D.F of the Gamma random variable in terms of the Poisson process.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Q(3.) (Continuation of Q2) If X1, X2,- ... are independent and identically distributed exponential random variables with parameter d and N is a geometric random variable with parameter p independent of the sequence X1, X2, ... (i.e P(N = n) = p(1 – p)"-1), then show that N Y = X; i=1 is exponentially distributed with parameter Ap using conditioning arguments directly with the random sum, instead of using the m.g.f. method. Hint: Write the C.D.F of the Gamma random variable in terms of the Poisson process.
Transcribed Image Text:Q(3.) (Continuation of Q2) If X1, X2,- ... are independent and identically distributed exponential random variables with parameter d and N is a geometric random variable with parameter p independent of the sequence X1, X2, ... (i.e P(N = n) = p(1 – p)"-1), then show that N Y = X; i=1 is exponentially distributed with parameter Ap using conditioning arguments directly with the random sum, instead of using the m.g.f. method. Hint: Write the C.D.F of the Gamma random variable in terms of the Poisson process.
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