The number of train passengers who fail to pay for their tickets in a certain region has a poison distribution with a mean of 4 per train
i) all passengers pay their ticket?
ii) More than 1 passenger fail to pay for their tickets
If there are 4800 trains per month in the region,
iii) Find the expected number of trains with at least 1 non paying passenger.
iv) Calculate the average cost to the train company during a month if the average cost of a ticket is $12.54
iii) X is the random variable number of non-paying passengers on a train.
X ~ Poisson(mean = 4).
Let Y be the random variable number of trains with at least one non-paying passenger.
Then Y ~ Binomial(n = 4800, p = 0.98168)
where .
Then E(Y) = np ( ) = .....
iv) (Answer to iii)($12.54) = .....