# Questions tagged [exponential-distribution]

To be used for questions on using, finding, or otherwise relating to Exponential Distributions.

37 questions
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### Let $U=\operatorname{min}\{X,Y\}$ and $V=\operatorname{max}\{X,Y\}$. Show that $V-U$ is independent of $U$.

Let $X$ and $Y$ be exponentially distributed random variables with parameter $1$ and let $U=\operatorname{min}\{X,Y\}$ and $V=\operatorname{max}\{X,Y\}$. Show that $V-U$ is independent of $U$. We ...
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### Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.

Let $X, Y$ be an exponentially distributed random variables with parameters $a, b$. Then $X$ has pdf: $$f_X(x) =\begin{cases} a e^{-a x},& x\geq 0\\ 0,& \text{otherwise}.\end{cases}$$ ...
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### How to prove that geometric distributions converge to an exponential distribution?

How to prove that geometric distributions converge to an exponential distribution? To solve this, I am trying to define an indexing $n$/$m$ and to send $m$ to infinity, but I get zero, not some ...
177 views

### Expected sum of exponential variables until two of them sum to a threshold

In answering finding Expected Value for a system with N events all having exponential distribution, I somehow missed the fact that the OP wanted the expected value conditional on the number of events. ...
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### Expected time for the queue to become empty.

Question: Suppose, there is a queue A having i customers initially. The service time of the queue is Exponentially distributed with parameter $\mu$ (i.e., mean service time of one customer in Queue A ...
241 views

### Expectation of maximum of arithmetic means of i.i.d. exponential random variables

Given the sequence $(X_n), n=1,2,...$, of iid exponential random variables with parameter $1$, define: $$M_n := \max \left\{ X_1, \frac{X_1+X_2}{2}, ...,\frac{X_1+\dots+X_n}{n} \right\}$$ I want ...
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### Confused as to How I should Interpret the Exponential Distribution and its Probability Density Function

I'm confused as to how I should be interpreting the exponential distribution and its probability density function (PDF). I'm specifically referring to the fact that it peaks close to $x = 0$ and then ...