# Homewok 3

Let y_1, y_2, ..., y_I be independent and identically distributed as a poisson with rate lambda

1. Draw a graph of the density for a few values of lambda

2. What is an expression for the mean

3. What types of phenomena may the poisson be used to model?

Assume a gamma prior for lambda with shape alpha and rate beta.

4. Draw a graph of the density of the gamma for a few values of alpha and beta.

5. What is the prior mean in terms of alpha and beta?

6. What is the posterior distribution of lambda?

7. What is the posterior mean.

Suppose we are modeling the number of spikes on a set of 8 sensors.

Suppose the numbers of spikes are 2,10,1,3,15,7,0,5

8. Plot your posterior and prior beliefs.