Homework Help is Here – Start Your Trial Now!
Math
Statistics
1. A bus company manager is interested in estimating the expected daily expense, 0, which is defined as 0 = 3X+10. Here, A is the expected number of daily customers, and 10 corresponds to daily fixed costs. She assumes that the daily customers X₁,..., Xn are independent and identically distributed Poisson (A) random variables. She observes = 52 from a sample of n = 100 days. (a) (b) (c) (d) Write down the likelihood and log-likelihood functions for 0. Use the log-likelihood from the previous question to prove that the maximum likehood estimator for is = 3X + 10. What is the estimated daily expense? Prove that is unbiased for and find its mean squared error. Prove that is consistent for 0.

1. A bus company manager is interested in estimating the expected daily expense, 0, which is defined as 0 = 3X+10. Here, A is the expected number of daily customers, and 10 corresponds to daily fixed costs. She assumes that the daily customers X₁,..., Xn are independent and identically distributed Poisson (A) random variables. She observes = 52 from a sample of n = 100 days. (a) (b) (c) (d) Write down the likelihood and log-likelihood functions for 0. Use the log-likelihood from the previous question to prove that the maximum likehood estimator for is = 3X + 10. What is the estimated daily expense? Prove that is unbiased for and find its mean squared error. Prove that is consistent for 0.

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
See similar textbooks
icon
Related questions
Question
1. A bus company manager is interested in estimating the expected daily expense, 0, which is defined as 0 = 3X+10. Here, X is the expected number of daily customers, and 10 corresponds to daily fixed costs. She assumes that the daily customers X₁,..., Xn are independent and identically distributed Poisson (X) random variables. She observes = 52 from a sample of n = 100 days. (a) (b) (c) (d) Write down the likelihood and log-likelihood functions for 0. Use the log-likelihood from the previous question to prove that the maximum likehood estimator for 0 is = 3X + 10. What is the estimated daily expense? Prove that is unbiased for and find its mean squared error. Prove that is consistent for 0.
Transcribed Image Text:1. A bus company manager is interested in estimating the expected daily expense, 0, which is defined as 0 = 3X+10. Here, X is the expected number of daily customers, and 10 corresponds to daily fixed costs. She assumes that the daily customers X₁,..., Xn are independent and identically distributed Poisson (X) random variables. She observes = 52 from a sample of n = 100 days. (a) (b) (c) (d) Write down the likelihood and log-likelihood functions for 0. Use the log-likelihood from the previous question to prove that the maximum likehood estimator for 0 is = 3X + 10. What is the estimated daily expense? Prove that is unbiased for and find its mean squared error. Prove that is consistent for 0.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 7 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS