A travel agency is conducting an experiment, where they ask people in the street one-by- one whether they have travelled overseas in the last year. The number of people they ask until they find the first person who answers 'Yes', X = {1, 2, 3, ...}, can be explained by a Geometric distribution, with probability mass function Pr(X = k) = (1 − p)k-¹p, k={1,2,3,...}, 0
A travel agency is conducting an experiment, where they ask people in the street one-by- one whether they have travelled overseas in the last year. The number of people they ask until they find the first person who answers 'Yes', X = {1, 2, 3, ...}, can be explained by a Geometric distribution, with probability mass function Pr(X = k) = (1 − p)k-¹p, k={1,2,3,...}, 0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![A travel agency is conducting an experiment, where they ask people in the street one-by-
one whether they have travelled overseas in the last year. The number of people they ask
until they find the first person who answers 'Yes', X = {1, 2, 3, ...}, can be explained by a
Geometric distribution, with probability mass function
Pr(X= k) = (1 - p)k-¹p, k = {1, 2, 3, ...}, 0<p<1,
where p is the probability of receiving a positive answer. They carry out this experiment
n times and record the number of people they ask each time until they receive a positive
answer, i.e. they have observations x₁, x2,
...g Xn.
(a) Write down the likelihood and show that the maximum-likelihood estimator for p is
equal to
n
1
P
=
-
n
X
ΣXi
i=1
(b) The travel agency visited 6 different places and obtained the following results for their
experiment: 5, 8, 3, 6, 8, 9. What is the maximum-likelihood estimate for p based on these
values and how would you interpret it?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb3eb6f5-ad7a-4565-9bbe-4e7695b0b0f2%2F389f0fcd-b1a7-47f4-9507-b9796a8b902a%2Fnaizwm_processed.png&w=3840&q=75)
Transcribed Image Text:A travel agency is conducting an experiment, where they ask people in the street one-by-
one whether they have travelled overseas in the last year. The number of people they ask
until they find the first person who answers 'Yes', X = {1, 2, 3, ...}, can be explained by a
Geometric distribution, with probability mass function
Pr(X= k) = (1 - p)k-¹p, k = {1, 2, 3, ...}, 0<p<1,
where p is the probability of receiving a positive answer. They carry out this experiment
n times and record the number of people they ask each time until they receive a positive
answer, i.e. they have observations x₁, x2,
...g Xn.
(a) Write down the likelihood and show that the maximum-likelihood estimator for p is
equal to
n
1
P
=
-
n
X
ΣXi
i=1
(b) The travel agency visited 6 different places and obtained the following results for their
experiment: 5, 8, 3, 6, 8, 9. What is the maximum-likelihood estimate for p based on these
values and how would you interpret it?
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