Question: A particular website generates income when people visiting the site click on ads. The number of people visiting the website is modeled as a Poisson process with rate α = 30 per second. Of those visiting the site, 60% click on an ad. Let Y denote the number of those who will click on an ad over the next minute.
(a) The distribution of the random variable Y is (choose one)
(i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson. (Hint. See Example)
(b) Give the mean and variance of Y.
(c) Use R commands to find the probability that Y > 1100.
Example: People enter a department store according to a Poisson process with rate α per hour. It is known that 30% of those entering the store will make a purchase of $50.00 or more. Find the probability mass function of the number of customers who will make purchases of $50.00 or more during the next hour.