The percentage of Americans who claim to have no religious affiliation is the highest since 1930, approximately 20%.40 In a group of 30 police officers, 6 have no religious affiliation. Suppose 4 officers from this group are selected at random.
a. What is the probability that exactly 1 officer will have no religious affiliation?
b. What is the probability that at most 2 officers will have no religious affiliation?
c. Suppose the group consists of 50 police officers, 10 with no religious affiliation. Find the probabilities in parts (a) and (b) given this new, larger group.
d. Suppose 4 officers are selected at random from across the country. What is the probability that exactly 1 will have no religious affiliation? At most 2 will have no religious affiliation?
e. Compare all of these probabilities. Explain how the hypergeometric distribution is related to the binomial distribution.
Suppose X is a Poisson random variable with l 5 2. Let the random variable Y have a probability distribution as given in the following table.
Find the expected value of Y. Suppose the distribution of Y is changed slightly, at the right tail, as given in the following table.
Find the expected value of Y.
Suppose the distribution of Y is changed again, once more at the right tail.
Find the expected value of Y.
Continue in this manner. To what number is E(Y) converging, and why does this make sense?