# Questions tagged [exponential-distribution]

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

215 questions
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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 ...
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### Find the distribution of $R=\bar X / \bar Y$ where $X$ and $Y$ are exponentially distributed

Find the distribution of $R=\bar X / \bar Y$ given that exponential distribution with mean parameter 2 is equivalent to Chi squared with 2 dof. I'm given 2 samples $x_i$ and $y_i$ of sizes $n$ ...
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### Showing random variables are independent

The question I am attempting is the one shown below: It is easy enough to find $F_U , F_V$ from definitions, and I have shown that $U \sim \epsilon (2)$ by subbing in to the expression for $F_U$. ...
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### Poisson bus arrival process with different arrival rate

I want to know what I am thinking is right. There are two types of buses, B1 and B2. The arrival rate of B1 is r1 and B2 is r2. The arrival of those buses are independent Poisson arrival process. ...
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### Find $\mathbb P \{ \max(X, Y) - \min(X, Y) \gt 0.2 \}$.

Let $X$ and $Y$ be iid random variables for which $X \sim \text{Expo}(2)$ and $Y \sim \text{Expo}(3)$. Find $\mathbb P \{ \max(X, Y) - \min(X, Y) \gt 0.2 \}$. SOLUTION: There is a clever way to ...
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### An exponential family problem

I don't know how to express the problem to the form $f(x|\theta)=h(x)c(\theta)(\sum_{i=1}^{k}\omega_i(\theta)t_i(x))$ Let $X$ have pdf $f(x)=\frac{1}{\beta}e^{-(x-\alpha)/\beta}$, $x>\alpha$ ...
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### Sufficiency in the exponential distribution

I am trying to show that given a random sample $\{X_i\}_{i=1}^n$ where $X_i\sim exp(\lambda^{-1})$, the statistic $T(\mathbf{X})=\sum_{i=1}^n X_i$ is sufficient by using only the definition. I have ...
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### Exponential Test

Given a collection of data points, without any other information I want to test for an exponential distribution. In a different case, I tested for normality using an Accord implementation of the ...
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### Probability $P\{\min{X_1,X_2}\leq X_3\}$?

Let $X_1, X_2$ and $X_3$ exponential random variables with the same parameter $\beta$? The PDF and CDF of $X_i$ are $$f_{X_i}(x)=\beta e^{-x \beta},$$ $$F_{X_i}(x)=1-e^{-x \beta}.$$ The PDF and ...