The pmf of a geometric distribution with parameter p is given by Р(1 — р)" п %3 0, 1, 2, ... otherwise. Pn Assume p> 0. Show that the variance is (1 – p)/p?. Hint: Eng" %3D (1 – q)² n=0 for |g| < 1.
The pmf of a geometric distribution with parameter p is given by Р(1 — р)" п %3 0, 1, 2, ... otherwise. Pn Assume p> 0. Show that the variance is (1 – p)/p?. Hint: Eng" %3D (1 – q)² n=0 for |g| < 1.
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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![4.
The pmf of a geometric distribution with parameter p is given
by
S p(1 – p)" n= 0, 1, 2, ...
otherwise.
Pn =
Assume p> 0. Show that the variance is (1 – p)/p². Hint:
Σ
Eng"
(1 – q)²
n=0
for |g| < 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2272493c-2da1-4ad8-b175-45fd09ab1d8e%2Fe3ef16e2-4710-4fc2-a3bb-728463d681b5%2Fx36gb6_processed.png&w=3840&q=75)
Transcribed Image Text:4.
The pmf of a geometric distribution with parameter p is given
by
S p(1 – p)" n= 0, 1, 2, ...
otherwise.
Pn =
Assume p> 0. Show that the variance is (1 – p)/p². Hint:
Σ
Eng"
(1 – q)²
n=0
for |g| < 1.
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