Chapters: Normal and Exponential random variables.Q: Let X be an exponential random variable with rate 1. If a and b arepositive numbers, then P(X > a + b|X > b) = P(X > a).a. Explain why this is called the memoryless propertyb. Show that for an exponential rv X with rate 1, P(X > a) = e-ad.

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Answered: Q: Let X be an exponential random…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Q: Let X be an exponential random variable with rate 1. If a and b are positive numbers, then P(X > a + b|X > b) = P(X > a). a. Explain why this is called the memoryless property b. Show that for an exponential rv X with rate 1, P(X > a) = e-al.