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### Difference of two exponential RVs [duplicate]

Let $X,Y$ be independent exponential RV's with respective pdf's $f(x) = \lambda e^{-\lambda x}$ and $f(y) = \mu e^{-\mu y}$. We want to find the pdf of $Z=X-Y$. I originally tried the convolution ...
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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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### How to Find CDF of $T_1-T_2$? [duplicate]

Given that $T_1, T_2$ are iid $\text{exp}(\lambda)$ variates. I want to find the cdf $F_T(t)$ where $T=T_1-T_2$ My Attempt $F_T(t) =_1 P(T<t) = P(T_1-T_2<t) = P(T_1<T_2 + t)$ Where $=_1$ is ...
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### Find PDF of $Y = X_1-X_2$ [duplicate]

$X_1$ and $X_2$ are i.i.d random variables and the pdf of each of them is $e^{-x}$ for $x>0$ and $0$ otherwise. $Y = X_1-X_2$ and the question asks to find the pdf for $Y$? I took the approach of ...
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### Waiting time: exponential distribution

Smith is waiting for his two friends Lee and Yang to visit his house. The time until Lee arrives is Exp($\lambda_1$) and the time until Yang arrives is Exp($\lambda_2$). After arrival, Lee stays an ...
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We are given two machines call them $M1$ and $M2$. $M2$ will be put in use at a time $t$ from now. The lifetime of machine $i$ is exponential with rate $\alpha_i$ $i=1,2$. What is the probability that ...