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What is E[X]? Prove that P[X>0] ≈ 1 - exp • (-(19) · - ). Describe how this could be used to obtain an estimator for the population size? (Your estimator does not need to be unbiased) (see Slide 9 of Lecture 11)

What is E[X]? Prove that P[X>0] ≈ 1 - exp • (-(19) · - ). Describe how this could be used to obtain an estimator for the population size? (Your estimator does not need to be unbiased) (see Slide 9 of Lecture 11)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. (Birthday problem) Let X count the number of collisions among k independent samples from a discrete uniform distribution over {1, 2,...,n}. a) What is E[X]? b) Prove that P[X>0] ≈ 1 exp • ( − (1) · ² ) . c) Describe how this could be used to obtain an estimator for the population size? (Your estimator does not need to be unbiased) (see Slide 9 of Lecture 11)
Transcribed Image Text:1. (Birthday problem) Let X count the number of collisions among k independent samples from a discrete uniform distribution over {1, 2,...,n}. a) What is E[X]? b) Prove that P[X>0] ≈ 1 exp • ( − (1) · ² ) . c) Describe how this could be used to obtain an estimator for the population size? (Your estimator does not need to be unbiased) (see Slide 9 of Lecture 11)
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