Question

Asked Oct 26, 2019

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Step 1

**Note:**

Hey there! Thank you for the question. Although the hint in the question suggests finding the pdf of *Y* to solve the problem, we have used a different method- the cdf- to solve it. Both ways are correct and possible to use here.

Step 2

**Introduction:**

Consider an exponential distribution with probability density function (pdf):

*f* (*x*) = *λ e ^{– λx}*;

The cumulative distribution function (cdf) for this distribution is:

*P* (*X* ≤ *x*) =* F* (*x*) = 1 – *e ^{– λx}*;

Therefore, the tail function is given as:

*P* (*X* > *x*) = *e ^{– λx}*;

Step 3

**Calculation:**

It is given that *Y* = *X*(1) = min {*X*1, *X*2, …, *Xn*}.

Note that, as *X*1, *X*2, …, *Xn* are independent, their joint cdf fill be the product of their individual cdf’s; as a result, their joint tail function would also be the product of their ind...

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