2. Find the first and second derivatives m'(t) and m"(t) of m(t) and calculate m(¹)(0) and m²) (0) and use hem to find the mean and variance o².
2. Find the first and second derivatives m'(t) and m"(t) of m(t) and calculate m(¹)(0) and m²) (0) and use hem to find the mean and variance o².
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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question 2 please
Transcribed Image Text:Consider the geometric distribution.
fx = (1-p)k-¹p
1. Show that the moment generating function is
where q = 1 - p.
Hint: You may assume that let(1 - p)| < 1.
Hint: Use the geometric series 1 k.
m(t) =
pet
1-qet
2.Find the first and second derivatives m' (t) and m"(t) of m(t) and calculate m(¹) (0) and m(2) (0) and use
them to find the mean μ and variance o².
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