This problem examines testing the fit of “experimental” data to known distribution.
See the class notes for how to generate a Poisson distribution.
a) Develop a script & supporting functions that performs the following.
a. Prompt the user for λ and N
b. Generate N RVs using the equation below. See the lecture notes for how to generate a Poisson RV and how to generate a discrete RV.
Z = X + Y where X ~ Poisson(λ) and
c. Plot a histogram of Z. Hint, I recommend using the hist command with the values of the bins selected by the script rather than letting the hist command select them.
d. Estimate λ using the Maximum Likelihood Estimator (MLE). The MLE for a Poisson distribution is the mean on the samples. Display the estimate of λ and the user input.
e. Extra Credit: Find M equi-probable intervals, estimate the Chi-squared parameter (see the lecture notes), and perform the chi-squared test. Hint, the probability of a
Poisson distribution between I and J is given by
b) Run the script with λ = 4, and N = 200. Record the output as part of your solution.
This question belongs to MATLAB software and discusses about application of MATLAB in statistics andto generate a Poisson distribution.
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