MATH 314 Homework 09

Due 2026-03-09 by 11:59pm

1. Suppose you have random variables which are independent (meaning you can multiply together the density function evaluations at each random variable) and identically distributed (all from the same distribution) from the Poisson distribution with unknown rate parameter . Find the maximum likelihood estimator for .

2. Using Python, pick a rate parameter for a Poisson distribution. Generate random numbers from this Poisson distirbution. Write a Python function that calculates the simplified, negative, log-likelihood of the Poisson distribution's density. You are to write out the function by hand, not using any scipy methods. Use the function scipy.optimization.minimize(...) to find an estimate of the rate parameter you chose above by minimizing the log-likelihood function you wrote.