please show me the last two questions: third and fourth A random variable X has an exponential distribution with parameter λ if its CDF equalse-xt,Fx(t) =10,=t> 0t≤0We denote this distribution Exp(\).(i) For 0 < p < 1, compute the 100p-th percentile of Exp(\), i.e. compute the quantilefunction (p).(ii) What is the median of Exp(\)?·92(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 YLet Yalso has an exponential distribution.An.···,(iv) In the setting of previous part, let Z = max(X₁, X2, Xn). Compute the CDF ofZ. Does Z have an exponential distribution?

Answered: Image /qna-images/answer/26893f11-1c27-4152-b674-afe76e8f1a62.jpg

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)

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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