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Will you please give me question paper for Institute of actuaries of india-subject ct3- probability and mathematical statistics examination Here I am giving you question paper for Institute of actuaries of india-subject ct3- probability and mathematical statistics examination in PDF file attached with it . You are the producer for the television show Actuarial Idol. Each year, 1000 actuarial clubs audition for the show. The probability of a club being accepted is 0.20. The number of members of an accepted club has a distribution with mean 20 and variance 20. Club acceptances and the number of club members are mutually independent. Your annual budget for persons appearing on the show equals 10 times the expected total number of persons plus 10 times the standard deviation of the total number of persons. Calculate your annual budget for persons appearing on the show. a) Determine the mean and standard deviation of this sample (6) Assume the following: • The distribution of weights of the filled packets are normal • The distribution of weights of the rejected packets are normal • The standard deviation of the whole distribution may be estimated as 4 times the standard deviation of this sample b) Using the fact that the overall probability to reject a package is 0.05: i) Show that an estimate of the mean weight of the whole distribution is 5.246 kg. (3) ii) Hence, estimate the mean weights of the packages which are not rejected. (1) [10] Q. 6) A lamp requires a particular type of light bulb whose lifetime has a distribution with mean 3 (months) and variance 1. As soon as a bulb burns out, it is replaced with a new one. What is the smallest number of bulbs you need to purchase so that, with probability at least 0.9772, the lamp burns for at least 40 months? A colleague points out that Company C has the largest mean premium of 165.2 and that Company B has the smallest mean premium of 131.4 and suggests performing t-test to compare these two companies. i) Perform this t-test, using the estimate of variance from the ANOVA table, and in particular show that there is a significant difference at the 1% level. ii) Your colleague states that there is therefore a significant difference between the six companies. Discuss the apparent contradiction with your conclusion in part (a). Last edited by Aakashd; June 25th, 2019 at 03:46 PM. |