1. Solve problem 1.13 in the textbook.
2. The Poisson distribution is where x is an integer value. The distribution satisfies E[x] = VAR[x] = λ.
(i) Calculate the maximum likelihood estimate of λ from an IID sample of size N: x1,…,xN. (ii) Calculate the mean and variance of the maximal likelihood estimator.
3. Solve problem 1.30 in the textbook.
4. Solve problem 2.10 in the textbook.
5. Solve problem 2.38 in the textbook. This repeats and completes some calculations from classfor the Bayesian treatment of the mean for the Gaussian variable.