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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question 3. Suppose there is a 24.50% chance each child will get influenza, whereas in 13.50% of two-child families both children get the disease. What is the probability that at least one child will get influenza? O a. 0.3550 O b.0.06 O c. 0.49 O d. 0.11
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