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Page 327, 5.1.7.* Let X₁, ...,Xn be iid random variables with common pdf f(x) exp{-(x-20)}, x > 20,- , -∞ < < ∞, f(x) = 0, elsewhere. This pdf is called the shifted exponential, shifted by 20.

Page 327, 5.1.7.* Let X₁, ...,Xn be iid random variables with common pdf f(x) exp{-(x-20)}, x > 20,- , -∞ < < ∞, f(x) = 0, elsewhere. This pdf is called the shifted exponential, shifted by 20.

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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Page 327, 5.1.7

Page 327, 5.1.7.* Let \( X_1, \ldots, X_n \) be iid random variables with common pdf \( f(x) = \exp\{-(x-2\theta)\} \), \( x > 2\theta, -\infty < \theta < \infty \), \( f(x) = 0 \), elsewhere. This pdf is called the shifted exponential, shifted by \( 2\theta \). Let \( Y_n = \min\{X_1, \ldots, X_n\} \). Prove that \( Y_n \rightarrow 2\theta \) in probability by first obtaining the cdf of \( Y_n \).
Transcribed Image Text:Page 327, 5.1.7.* Let \( X_1, \ldots, X_n \) be iid random variables with common pdf \( f(x) = \exp\{-(x-2\theta)\} \), \( x > 2\theta, -\infty < \theta < \infty \), \( f(x) = 0 \), elsewhere. This pdf is called the shifted exponential, shifted by \( 2\theta \). Let \( Y_n = \min\{X_1, \ldots, X_n\} \). Prove that \( Y_n \rightarrow 2\theta \) in probability by first obtaining the cdf of \( Y_n \).
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