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### Linear Combination of Exponential Random Variables [duplicate]

Let $Y \sim \exp(\delta)$ and $T \sim \exp(\lambda)$, and $Y$ and $T$ are independent. How do I get the density $f(x)$ where $X=Y-cT$, $c>0$? Thanks.
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### Finding the probability density function for IID rv [duplicate]

The question is as follows: Suppose that X1 and X2 are independent, identically distributed exponential random variables. Determine the PDF for for X1 - X2. I understand that because X1 and X2 are ...
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### PDF of |X-Y| where X,Y ~ exp($\lambda$)
I need to find the PDF of $Z=|Y-X|$ given that $X,Y\sim exp(\lambda)$ and both independent. What I did (I want to use the CDF and not convolutions): \$f_{X,Y}(x,y)=\cases{\lambda^2 e^{-\lambda(x+y)} &...