# Solution Library

# Generation of Poisson distributionUsing MATLAB

**Question**

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.

**Summary**

This question belongs to MATLAB software and discusses about application of MATLAB in statistics andto generate a Poisson distribution.

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