(a) There are six houses on Station Street, numbered 1 to 6. A courier has six parcels to deliver, one addressed to each house. The courier is in a hurry

and has no time to look at which parcel is delivered to which house (one per house). i. Explain in words why the probability that the people living in the first house receive the correct parcel is equal to 1/6. ii. Let X;, for i = 1, 2, ..., 6, be the random variable which is equal to 1 if the people living in house number i receive the correct parcel, and which is equal to 0 otherwise. Determine E(Xi). (b) R, T and X are independent random variables such that: R has a binomial distribution with n =10 and T = 0.3 • T has a Poisson distribution with lambda = 8 X has a normal distribution with mu5 and sigma = 0.3. Calculate the mean and variance of 2R – T+ 3X. (c) For the binomial distribution with a probability of success of 0.25 in an individual trial, calculate the probability that, in 50 trials, there are at least 8 successes using a normal approximation. ) The independent random variables X1 and X2 are each normally distributed with mean 1 and variance 4. Calculate: P\left(\left(4 X_{1}-3 X_{2}\right)^{2} \leq 25\right)