Hi, im confused why we are using the compound Poisson distribution here - the questions asks spend PER customer over the 2 ATM’s, so why would we be concerned with the number of customers (ie. Involving the poisson part of the question) . If we are only concerned in the amount withdrawn wouldn’t it just be a case of combining the 2 normal distributions? thanks in advance
Hello Here the Examiners wanted us to calculate the probability that an individual withdrawal is less than 1,400. Indeed we can answer this without explicitly thinking about the compound distributions. We have: P(W < 1400) = P(W < 1400, Machine 1) + P(W < 1400, Machine 2) = P(W < 1400 | Machine 1)P(Machine 1) + P(W < 1400 | Machine 2)P(Machine 2) P(W < 1400 | Machine 1) is the probability that a realisation from the N(1500, 300^2) distribution is less than 1400. P(W < 1400 | Machine 2) is the probability that a realisation from the N(1000, 200^2) distribution is less than 1400. P(Machine 1) = 20/(20 + 50) P(Machine 2) = 50/(20 + 50) Hope this helps! Andy
