a) Suppose two people set up a meeting at noon, and each anives at a time uniformly distributed between noon and 12:30pini What is the probability that the first person to anive waits more than 10 minutes for the other? (4 marks) b) Let X], X,,..X, be a random sample of size n from a gamma distribution with parameters o =1 and p =1.What is the distribution of the sample mean X ? (5 Marks) ci Consider a bivariate normal density f(x, x) -Ce70 where Q=16X + X - 4xX Determine: (i) the mean vector / and variance-covariance matrix ) . (5 Marks) (ii) the constant C. (2 Marks) (iii) the conditional density of X, given X, . (4 Marks) d) Let Y1