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function Q(p). (ii) What is the median of Exp(\)? (iii) Suppose X₁, X2,..., Xn are independent exponential RV's with parameters X₁, A2,..., An. Let Y = ,Xn). Compute the CDF of Y and use this to show that Y min(X₁, X₂, also has an exponential distribution. (iv) In the setting of previous part, let Z = max(X₁, X₂, Xn). Compute the CDF of Z. Does Z have an exponential distribution?

function Q(p). (ii) What is the median of Exp(\)? (iii) Suppose X₁, X2,..., Xn are independent exponential RV's with parameters X₁, A2,..., An. Let Y = ,Xn). Compute the CDF of Y and use this to show that Y min(X₁, X₂, also has an exponential distribution. (iv) In the setting of previous part, let Z = max(X₁, X₂, Xn). Compute the CDF of Z. Does Z have an exponential distribution?

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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please show me the last two questions: third and fourth

A random variable X has an exponential distribution with parameter λ if its CDF equals e-xt, Fx(t) = 1 0, = t> 0 t≤0 We denote this distribution Exp(\). (i) For 0 < p < 1, compute the 100p-th percentile of Exp(\), i.e. compute the quantile function (p). (ii) What is the median of Exp(\)? · 9 2 (iii) Suppose X₁, X2, Xn are independent exponential RV's with parameters A₁, A2, min(X₁, X₂, ..., Xn). Compute the CDF of Y and use this to show that Y Let Y also has an exponential distribution. An. ···, (iv) In the setting of previous part, let Z = max(X₁, X2, Xn). Compute the CDF of Z. Does Z have an exponential distribution?
Transcribed Image Text:A random variable X has an exponential distribution with parameter λ if its CDF equals e-xt, Fx(t) = 1 0, = t> 0 t≤0 We denote this distribution Exp(\). (i) For 0 < p < 1, compute the 100p-th percentile of Exp(\), i.e. compute the quantile function (p). (ii) What is the median of Exp(\)? · 9 2 (iii) Suppose X₁, X2, Xn are independent exponential RV's with parameters A₁, A2, min(X₁, X₂, ..., Xn). Compute the CDF of Y and use this to show that Y Let Y also has an exponential distribution. An. ···, (iv) In the setting of previous part, let Z = max(X₁, X2, Xn). Compute the CDF of Z. Does Z have an exponential distribution?
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