Let X1 and X2 be two independent and identically distributed random variables with N(µ, 1) distribution. Calculate the conditional distribution X1 | {X1 + X2 = s}.

What is the distribution of X + Y when X and Y are independent random variables with uniform distribution in (0, 1)?

Find P(X=3)

Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.