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Derive the variance for the geometric.

Derive the variance for the geometric.

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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1. Derive the variance for the geometric. 2. Show that the first derivative of the moment generating function of the geometric evaluated at 0 gives you the mean. 3. Let X be distributed as a geometric with a probability of success of 0.15. a. Give a truncated histogram (obviously you cannot put the whole sample space on the x-axis of the histogram) of this random variable. b. Give F(x) c. Find the probability it takes 10 or more trials to get the first success. d. Here is a challenge. What is the probability that it takes an even number of trials to get the first success, i.e., P(X=2,4,6,8,...)
Transcribed Image Text:1. Derive the variance for the geometric. 2. Show that the first derivative of the moment generating function of the geometric evaluated at 0 gives you the mean. 3. Let X be distributed as a geometric with a probability of success of 0.15. a. Give a truncated histogram (obviously you cannot put the whole sample space on the x-axis of the histogram) of this random variable. b. Give F(x) c. Find the probability it takes 10 or more trials to get the first success. d. Here is a challenge. What is the probability that it takes an even number of trials to get the first success, i.e., P(X=2,4,6,8,...)
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