Derive the variance for the geometric.
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,...)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa46b3375-7c9a-4321-a72c-4cbd34a6c9e9%2Faf8ad923-267b-40a7-827d-6a9b98673a3b%2Ftqlczs_processed.png&w=3840&q=75)
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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