Suppose we are interested in the number of people in a small town of 20,000 people with a rare disease which affects 1 in 100,000 people each with equal probability. (4 points each)

4)What is the probability that no people in the town have this disease?

5)What is the probability that 2 or fewer people in the town have this disease?

( FYI, the first three questions are as follows, but you don't need to answer, thank you!)

1)What is the exact distribution of the number of people in the town with this disease? By exact I mean without making an approximation. Let X be the number of with the rare disease in the small town.

2) What is the expected number of people in the town with the disease?

3)You wish to use a Poisson approximation to estimate the probability distribution. What are the two criteria required to use this approximation? Show that they are met.