MAY I know how to get the final answer?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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MAY I know how to get the final answer?

If X,, X2, ..., Xn are independent random variables having exponential distributions with the same
п
parameter 0.
(а)
Find the probability density of the random variable Y = X1 + X2 + …+ Xn.
...
(b) Identify the distribution of Y, and what are its parameters?
Transcribed Image Text:If X,, X2, ..., Xn are independent random variables having exponential distributions with the same п parameter 0. (а) Find the probability density of the random variable Y = X1 + X2 + …+ Xn. ... (b) Identify the distribution of Y, and what are its parameters?
Solution
Since X1, X2, .,Xn having exponential distribution with the same
parameter 0, hence
1
Mx, (t)
Ot
1
Mx, (t)
1 — Өt
1
Mx, (t)
1 – Ot
Based on Theorem 1.27,
n
My(t) = | | Mx;(t)
i=1
Ot,
Ot
Ot
(1 – Ot)n
Therefore, Y has gamma distribution with parameter a = n and ß = 0.
Transcribed Image Text:Solution Since X1, X2, .,Xn having exponential distribution with the same parameter 0, hence 1 Mx, (t) Ot 1 Mx, (t) 1 — Өt 1 Mx, (t) 1 – Ot Based on Theorem 1.27, n My(t) = | | Mx;(t) i=1 Ot, Ot Ot (1 – Ot)n Therefore, Y has gamma distribution with parameter a = n and ß = 0.
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