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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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QUESTION: Let $X$ and $Y$ be exponentially distributed random variables with parameters $a$ and $b$ respectively. Calculate the following probabilities: (a) $P(X>a)$ (b) $P(X>Y)$ (c) $P(X>Y+... 1answer 733 views ### Waiting time: exponential distribution Smith is waiting for his two friends Lee and Yang to visit his house. The time until Lee arrives is Exp($\lambda_1$) and the time until Yang arrives is Exp($\lambda_2$). After arrival, Lee stays an ... 1answer 387 views ### Probability of a sequence of events in a Poisson process. I am starting to study Poisson processes and I came up with this question: Let there be two Poisson processes with rates$\lambda$and$\mu$respectively, monitoring the occurrence of events (e.g. ... 3answers 287 views ### pdf for a difference of exponential random variables Suppose$X$is an exponential random variable with mean$2$, and$Y$is an exponential random variable with mean$3$. I want to write the density function for$X-Y$. Now, I know (at least, I'm pretty ... 1answer 229 views ### Difference of Exponential Random Variables / Linear Transformations of RVs Suppose X and Y are both distributed exponentially with parameter$\lambda$and$\mu$respectively. I am trying to find the distribution of X - Y via this method and it does not seem to be working, ... 1answer 151 views ### Probability with exponential random variable Machine$1$is currently working. Machine$2$will be put in use at time$t$from now. If the lifetime of machine$i$is exponential with rate$\lambda_i=1,2$, what is the probability that machine ... 0answers 206 views ### Expected value (waiting time) of two independent exponentially distributed arrival times occuring in a given distance Suppose we have two independent exponentially distributed arrival times X1, X2 having rates λ and μ. This means their corresponding expected waiting times are 1/λ and 1/μ accordingly. Now I'm ... 1answer 105 views ### Is the distribution of one exponential will be smaller than a second one Uniform? I came by an expression which I am not sure I understand. If:$X_1 \sim exp(\lambda)X_2 \sim exp(\lambda)$Then:$P(X_1<X_2|X_2) \sim Uniform(0,1)$Where it is not clear to me what "$|X_2$... 2answers 49 views ### 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)} &...
We know that $X\sim \exp(1),Y\sim \exp(2)$ and they are independent. What is $P(Y>X)$? exp=Exponential... Thank you!
When I read maths chapter, I found following conditional probability expression in a part of intermediate step and then directly gave the answer $$I=\Pr\{x\leq y|x=t\}$$ ...