Answer the following questions correctly. Thanks in advance.

Question 5.1 Show that S-, the sample variance of a random sample, is an unbiased estimator of the population variance o [3] Question 5.2 (i) In a simple linear regression model the correlation coefficient has been calculated to be -0.28. Describe what this tells you about the relationship between the response and the explanatory variable. [1] (ii) Calculate the coefficient of determination in this case. Explain what the coefficient of determination measures. [2] [Total 3] Question 5.3 The random variable A has a Poisson distribution with mean 1. Y is a continuous random variable such that the conditional distribution of Y | / is uniform on the range (-N,2N) . Find expressions for E[Y] and var[Y]. [3] Question 5.4 A small financial consultancy with 120 clients has estimated the probability that any given existing client will take out a new policy in any given year to be 42%. Calculate the approximate probability that in the next year the consultancy will issue more than 62 new policies to its existing clients, stating any assumptions you make. [4]