I was doing practice questions of probability. I was able to do the first 2 parts of this question but I don't understand how to go about the last part.
An instructor gets her students A and B to type out his research papers. Both students make errors while typing according to a Poisson distribution. A makes errors at the rate of j per page, while B makes errors at the rate of k per page. Let the random variable F be the number of errors on a randomly chosen page.
a) If the students each do half of the total typing, what is the PMF of F?
b) What is the PMF of F if B types 70% of the pages?
c) What is var(F) for the PMF in part (a)?
My answers for the first two parts:
F = number of erros on a randomly chosen page
a) 0.5*(exp(-j) . (j) ^ f)/ f! + 0.5*(exp(-k) . (k) ^ f)/ f!
b) 0.3*(exp(-j) . (j) ^ f)/ f! + 0.7*(exp(-k) . (k) ^ f)/ f!