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1. The Poisson distribution is often used to describe how many times an event takes place within a certain time interval, such as number of daily customers at a store. Assume x1,..., xn ~iid Poisson(A), where X is the rate of occurrences. Calculate the maximum likelihood estimator of A with pen and paper or LaTeX, showing your work. The probability mass function (PMF) for the Poisson distribution is: f(x|A) = x!

1. The Poisson distribution is often used to describe how many times an event takes place within a certain time interval, such as number of daily customers at a store. Assume x1,..., xn ~iid Poisson(A), where X is the rate of occurrences. Calculate the maximum likelihood estimator of A with pen and paper or LaTeX, showing your work. The probability mass function (PMF) for the Poisson distribution is: f(x|A) = x!

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
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For question 1 just write the answer in a text file but for question 2 use 'R' language and code in r studio using the answer from question 1.

 

1. The Poisson distribution is often used to describe how many times an event takes place within a certain time interval, such as number of daily customers at a store. Assume x1,..., Xn viid Poisson(A), where A is the rate of occurrences. Calculate the maximum likelihood estimator of A with pen and paper or LaTeX, showing your work. The probability mass function (PMF) for the Poisson distribution is: f (x|A) = x! 2. With R, generate data from Poisson(A = 4) with rpois, then use optim to estimate A via the log-likelihood function for the Poisson distribution. Show your work. NOTE: You can take the log-likelihood function you found in the first question and convert that to something RStudio can understand.
Transcribed Image Text:1. The Poisson distribution is often used to describe how many times an event takes place within a certain time interval, such as number of daily customers at a store. Assume x1,..., Xn viid Poisson(A), where A is the rate of occurrences. Calculate the maximum likelihood estimator of A with pen and paper or LaTeX, showing your work. The probability mass function (PMF) for the Poisson distribution is: f (x|A) = x! 2. With R, generate data from Poisson(A = 4) with rpois, then use optim to estimate A via the log-likelihood function for the Poisson distribution. Show your work. NOTE: You can take the log-likelihood function you found in the first question and convert that to something RStudio can understand.
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