10 4. Members of a photographic group may enter a maximum of 5 photographs into a members only competition. Past experience has shown that the number of photographs, N, entered by a member follows the probability distribution shown below. n 0 1 2 3 4 5 P(N = n) a 0.2 0.05 0.25 b c Given that E(4N + 2) = 14.8 and P(N = 5½N > 2) = 1 2 (a) show that Var(N) = 2.76 (6) The group decided to charge a 50p entry fee for the first photograph entered and then 20p for each extra photograph entered into the competition up to a maximum of £1 per person. Thus a member who enters 3 photographs pays 90p and a member who enters 4 or 5 photographs just pays £1 Assuming that the probability distribution for the number of photographs entered by a member is unchanged, (b) calculate the expected entry fee per member. (3) Bai suggests that, as the mean and variance are close, a Poisson distribution could be used to model the number of photographs entered by a member next year. (c) State a limitation of the Poisson distribution in this case. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________