Q4. Consider the geometric distribution. fx = (1-p)k-1p 1. Show that the moment generating function is m(t) where q = 1-p. Hint: You may assume that let (1-p)| < 1. Hint: Use the geometric series 1 k. pet 1- qet

Q4. Consider the geometric distribution. fx = (1-p)k-1p 1. Show that the moment generating function is m(t) where q = 1-p. Hint: You may assume that let (1-p)| < 1. Hint: Use the geometric series 1 k. pet 1- qet

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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Question

Please help with the following question with full working.

Q4.
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 rk².
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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Follow-up Question

Please do question 2 from the image with full handwritten working.

Q4.
Consider the geometric distribution.
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 1².
fx = (1-p)k-1p
18
2k=1
m(t) =
1
pet
get
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 and variance o².

Solution

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