Question

1. Recall problem 1 from Assignment 4: Assume that the number of eggs laid by an insect is a Poisson variable with parameter X. Assume, furthermore, that every egg has a probability p to develop into an insect. What is the probability that eractly k insects will survive? You should have observed the fact that the number of surviving insects is a Poisson random variable with rate Ap. This time, use the law of total expectation and prove directly, without using the result you obtained in Assignment 4, that the expected number of surviving insects must be Ap

Answer 1