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2 5.8 Let R G(p) and define SR = 1 X₁, where X₁, X2,... is a sequence of iid Exp(A) random variables that are independent of R. a) Show, that SR Exp(p). [Hint: The easiest way is to use transform methods and conditioning.] b) For A = 1 and p = 1/10, estimate P(SR > 10) using CMC with a sample size of N = 1000. c) Repeat b), now using the conditional Monte Carlo estimator (5.22). Com- pare the results with those of a) and b). ~ خير ماريون

2 5.8 Let R G(p) and define SR = 1 X₁, where X₁, X2,... is a sequence of iid Exp(A) random variables that are independent of R. a) Show, that SR Exp(p). [Hint: The easiest way is to use transform methods and conditioning.] b) For A = 1 and p = 1/10, estimate P(SR > 10) using CMC with a sample size of N = 1000. c) Repeat b), now using the conditional Monte Carlo estimator (5.22). Com- pare the results with those of a) and b). ~ خير ماريون

A First Course in Probability (10th Edition)
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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2 5.8 Let R G(p) and define SR = 1 X₁, where X₁, X2, ... is a sequence of iid Exp(A) random variables that are independent of R. a) Show, that SR Exp(p). [Hint: The easiest way is to use transform methods and conditioning.] b) For A = 1 and p = 1/10, estimate P(SR > 10) using CMC with a sample size of N = 1000. c) Repeat b), now using the conditional Monte Carlo estimator (5.22). Com- pare the results with those of a) and b). N خير ماريون
Transcribed Image Text:2 5.8 Let R G(p) and define SR = 1 X₁, where X₁, X2, ... is a sequence of iid Exp(A) random variables that are independent of R. a) Show, that SR Exp(p). [Hint: The easiest way is to use transform methods and conditioning.] b) For A = 1 and p = 1/10, estimate P(SR > 10) using CMC with a sample size of N = 1000. c) Repeat b), now using the conditional Monte Carlo estimator (5.22). Com- pare the results with those of a) and b). N خير ماريون
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