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Let X exp(A) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t + s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?

Let X exp(A) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t + s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?

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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Let X~ exp(X) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t+s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?
Transcribed Image Text:Let X~ exp(X) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t+s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?
Let X~ exp(X) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t+s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?
Transcribed Image Text:Let X~ exp(X) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t+s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?
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