Solve the financial questions.
The punctuality of trains has been investigated by considering a number of train journeys. In the sample, 60%% of trains had a destination of Manchester, 20% Edinburgh and 20% Birmingham. The probabilities of a train arriving late in Manchester, Edinburgh or Birmingham are 30%, 20% and 25%, respectively. A late train is picked at random from the group under consideration. Calculate the probability that it terminated in Manchester. 2 A random variable X has a Poisson distribution with mean 1, which is initially assumed to have a chi-squared distribution with 4 degrees of freedom. Determine the posterior distribution of 1 after observing a single value x of the random variable X . 3 The number of claims in a week arising from a certain group of insurance policies has a Poisson distribution with mean /. Seven claims were incurred in the last week. The prior distribution of / is uniform on the integers 8, 10 and 12. (i) Determine the posterior distribution of / . Calculate the Bayesian estimate of / under squared error loss. 4 For the estimation of a population proportion p, a sample of n is taken and yields x successes. yle A suitable prior distribution for p is beta with parameters 4 and 4. (i) Show that the posterior distribution of p given x is beta and specify its parameters. [2] (Wi) Given that 11 successes are observed in a sample of size 25, calculate the Bayesian estimate under all-or-nothing (0/1) loss. [4] [Total 6] 5 The annual number of claims from a particular risk has a Poisson distribution with mean / . The yle prior distribution for # has a gamma distribution with a = 2 and 1 = 5. Claim numbers x1..... x, over the last n years have been recorded. () Show that the posterior distribution is gamma and determine its parameters. [3] Given that n =8 and > x; =5 determine the Bayesian estimate for / under: (a) squared-error loss (b) all-or-nothing loss4 Which of the following would NOT explain why the PE ratio of a particular company may stand above the average PE ratio of other companies? the company's shares are overvalued earnings are perceived to be relatively risky historical earnings are unusually low potential earnings growth is very high [2] The next three questions refer to PRP Ltd. The following details were extracted from the company's accounting records: Pre-tax profit 57,000 Tax paid 1,200 Depreciation 2,100 Inventories held at the beginning of the year 42,100 Inventories held at the end of the year 46,500 12% Loan stock 15,000 Revenue 103,250 Share capital and reserves 425,000 Non-current assets 55,000 5 PRP's return on capital employed was: 12.68% 12.95% 13.36% on 13.84% [2] 6 Relative to its revenue, PRP's average inventory turnover period was: 149 days 154 days 157 days 160 days [2] 7 The figure for 'net cash generated from operating activities' shown in PRP's cashflow statement was: E51,700 E53,500 656,500 E58,800 [2]
