# Questions tagged [exponential-distribution]

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

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### Knowing if two random variables are independent or not [closed]

Consider three independent random variables $X$, $Y$, and $Z$. Here, $X$ and $Y$ are i.i.d exponential random variables with parameter $\lambda$, and $Z$ is an exponential random variable with ...
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### The Cauchy-Stieltjes transform of the exponential distribution

I'm interested in the integral $$G(z)=\int_\mathbb{R} \frac{ce^{-cx}\mathrm{d}x}{z-x}$$ which defines the Cauchy-Stieltjes transform of the exponential distribution parameterized by some real $c>0$....
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### one-dimensional regular exponential family

I have got the question: Let $X$ and $Y$ be independent and exponentially distributed random variables with $E(X) = \mu$ and $E(Y) = 2\mu$, where $\mu > 0$. Represent the family of joint ...
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### Finding lambda in exponential distribution

I have the time data I hold in hours for 15 days. I want to calculate P(x>1.5) with exponential distribution in line with these data, but I am not sure how to find lambda value. Should it be (the ...
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### independence of exponential random variable and general independency

Maybe this is not a good enough question, but a long search on the internet led me to post the question here. Let's say we have three independent Poisson processes that are essentially the "...
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### How to solve the probability that customer C1 is the last to withdraw from the bank?

Consider a bank with two clerks. Three people, $C_1$, $C_2$, and $C_3$, enter simultaneously. $C_1$ and $C_3$ go directly to the clerks, and $C_3$ waits until either $C_1$ or $C_2$ leaves before he ...
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### What is the joint distribution of exponential random variables $T_1$ and $T_2$ when they are related as $T_2 = \max(T_1 - A_2, 0) + S_2$?

Suppose $T_{1}$ and $T_2$ are identically distributed RVs according to an exponential distribution of rate $\mu - \lambda$, $A_{2}$ is an exponential random variable with rate $\lambda$ and $S_2$ is ...
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### If I have hypoexponential interarrival times, then does it fulfill a poisson process?

My doubt arose when I wanted to add two independent exponential interarrival times of parameter $\lambda$ and $\gamma$ respectively, with $\gamma \neq \lambda$. I know that the sum of two independent ...