4 Unusually long: An instructor decides to make a grand assignment for a probability course. Given previous data, he believes that if two people work in pairs and divide the work equally, the time taken for each person could be modelled by an Exponential random variable with mean 10 hours. Let X1 be the time for the first person in the pair to be done with their work, and similarly X2 be the time for the second person in the pair to be done with their work. Assume that X1, X2 are independent. a) Find the joint PDF fx,X2(1, r2). b) Find the probability that the grand assign ment is done in less than 50 hours. P(X1+X2 < 50). c) took more than 50 hours. Using expectation, argue whether this is indeed what the instructor should expect or was the assign ment more difficult for the students than the instructor expected (that is mean of exponential random variable should be higher).45 A fter the grand assign ment, the instructor finds out that there were 5 groups out of 50 that

4 Unusually long: An instructor decides to make a grand assignment for a probability course. Given previous data, he believes that if two people work in pairs and divide the work equally, the time taken for each person could be modelled by an Exponential random variable with mean 10 hours. Let X1 be the time for the first person in the pair to be done with their work, and similarly X2 be the time for the second person in the pair to be done with their work. Assume that X1, X2 are independent. a) Find the joint PDF fx,X2(1, r2). b) Find the probability that the grand assign ment is done in less than 50 hours. P(X1+X2 < 50). c) took more than 50 hours. Using expectation, argue whether this is indeed what the instructor should expect or was the assign ment more difficult for the students than the instructor expected (that is mean of exponential random variable should be higher).45 A fter the grand assign ment, the instructor finds out that there were 5 groups out of 50 that

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 50E: Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible...

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