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If T1 and T2 are independent exponential random variables, find the density function of R=T(2) - T(1). This...

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Statistics

If T1 and T2 are independent exponentialrandom variables, find the density function of R=T(2) -T(1).

This is for the difference of the order statistics not of thevariables, i.e. we are not looking forT2 - T1. It is implied that they are bothfrom the same distribution. I know that

fT(t) = λe-λt

fT(1)T(2)(t1,t2) = 2fT(t1)fT(t2) =2λ2 e-λ​​​​​​​t1e-λ​​​​​​​t2 , 0 < t1 2 and I need to find fR(r).

From Mathematical Statistics and Data Analysis by Rice, 3rdEdition, Question 79 from Chapter 3. The solution in the back ofthe book: \"Exponential (λ)\". I am not sure how to get to thatanswer.

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