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# GEM2900 Assignment 2 Complete Solution

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Date Created: 11/06/15

Assignment 2 Instructions This is the second of a series of assignments for this module Each correct answer to a queonn is worth two 2 marks This question sheet is available from the module workbin folder Please make sure that you submit your answers via the lVLE assessment facility Submission period Wednesday 1 Apr 1200 hrs to Wednesday 8 Apr 1200 hrs A maximum of two attempts will be allowed for this assessment However if you have made two attempts only the last attempt to this assessment will be graded Exercise 1 There are 40 multiple choice questions in a history test For each question there are 5 alternatives of which only one alternative is the correct answer 3 marks are awarded for each correct answer and 1 mark is deducted for each wrong answer Little John is taking this history test However he is not fully prepared For each ques on little John either knows the answer or he doesnt If he doesnt then he will guess the answer at random Suppose that he knows the answer to each question with probability 055 It IS assumed that he answers each question independently and attempts all the questions Let the random variable X denote the number of questions he answers correctly Then X is a and p Binomial distribution with parameters n Round your answer to two decimal places For example 300 312 010 Exercise 2 Little Johns expected score in the test mentioned in Exercise 1 is Round your answer to two decimal places For example 300 312 010 Exercise 3 A life insurance company estimates that the probability that an individual in a certain risk group will survive one year is 099 Such a person wishes to buy a 75000 oneyear term life insurance policy This means that if the person dies in the next year the company will pay 75000 Let C denote how much the insurance company charges for such a policy If X denotes the net prot to the company from selling the policy what is the probability function of X a fX X 099X 001X 75000 for 0 ampt X ampt 099 if X C b pX X 001 if X 75000 0 otherwise 099 if X C c pX x 001 if x C 75000 0 otherwise National University of Singapore Page 1 GEM2900 20142015 Semester ll Assignment 2 Exercise 4 For Exercise 3 the value that C should be for the expected net prot to be zero is Round your answer to two decimal places For example 300 312 010 Exercise 5 Suppose 10 people buy such a policy as mentioned in Exercise 3 Using the law of rare events or otherwise what is the approximate probability that exactly 2 of them die in the next year Pick the option closest to the answer a 01 b 03 c 05 d 07 e 09 Exercise 6 In 30 independent ips of a fair coin the expected number of runs in the sequence is Round your answer to two decimal places For example 300 312 010 Exercise 7 Investigators need to determine which of 500 adults have a certain medical condition that aects 2 of the population A blood sample is taken from each of the individuals Assume that the 500 adults are a random sample from the population at large Instead of testing all 500 blood samples investigators group the samples into 50 groups of10 each mix a little of the blood from each of the 10 samples in each group and test each of the 50 mixtures What is the probability that any such mixture will contain the blood of at least one diseased person and hence test positive Pick the option closest to the answer a 01 b 03 c 05 d 07 e 09 Exercise 8 In the 50 mixtures of blood as mentioned in Exercise 7 the expected number of mixtures that will test positive is Round your answer to two decimal places For example 300 312 010 ANSWERS HERE PLEASE 1 N40 p064 2 7680 3 Option C 4 750 5 Option a 6 1550 7 Option a 8 915

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