Suppose that the number of men who visit a website is Poisson, with mean 12 per minute, and the number of women who visit the same site is also Poisson, with mean 15 per minute. Assume that the number of men and women are independent.
a. During the next 10 seconds, what is the probability that 1 man and 2 women visit the site?
b. What is the expected number of people who visit the site in the next 5 minutes?
c. What is the variance of the total number of people who visit the site in the next 5 minutes?