Problem 4. In a generalization of the birthday problem, consider a box of N tickets. You sample n tickets with replacement. Let pn be the probability of the event that a duplicate ticket appears. Write down an exact expression for pn, and also find an approximation to it using log(1 + x) ≈ x for small x. Then, approximate how large n has to be in order for Pn ≥ 0.5 (your answer should be a function of N). What is the value of this function of N for N = 365?
Problem 4. In a generalization of the birthday problem, consider a box of N tickets. You sample n tickets with replacement. Let pn be the probability of the event that a duplicate ticket appears. Write down an exact expression for pn, and also find an approximation to it using log(1 + x) ≈ x for small x. Then, approximate how large n has to be in order for Pn ≥ 0.5 (your answer should be a function of N). What is the value of this function of N for N = 365?
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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