# Questions tagged [exponential-distribution]

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

644 questions
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### Question regarding Erlang distribution with shape parameter $k=2$ [on hold]

Let $X_i$ be i.i.d. random variables with the CDF $$F_{x_i}(x_i)=1-e^{-λx_i},\quad \quad x\geq 0.$$ Define $$X= X_1+X_2+....+X_k\ .$$ A theorem states that $X$ obeys the Erlang-k distribution ...
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### Let $x_1=\exp(\lambda_1),x_2=\exp(\lambda_2)$, $x_1, x_2$ are independent show $P(x_1<x_2)=\frac{\lambda_1}{\lambda_1+\lambda_2}$ [on hold]

Let $x_1=\exp(\lambda_1),x_2=\exp(\lambda_2)$, and $x_1, x_2$ are independent random variables. Show that $P(x_1<x_2)=\dfrac{\lambda_1}{\lambda_1+\lambda_2}$
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### Derive the probability density function of $Z = T_1 + T_2$.

Let $T_1$ be the waiting time until the first call in a call center and let $T_2$ be the waiting from the first call until the second call. Assume that both $T_1$ and $T_2$ have an exponential ...
According to Wikipedia (https://en.wikipedia.org/wiki/Conjugate_prior) the gamma distribution is a conjugate prior for the exponential distribution (with unknown rate-parameter, $\lambda$, and ...
### Find $E(\text{min}(X_1,X_2,X_3))$ where each $X_i$ is exponential with parameter $i$
I want to calculate $E(\text{min}(X_1,X_2,X_3))$ where $X_1\sim\text{exp}(1), \ X_2\sim\text{exp}(2)$ and $X_3\sim\text{exp}(3).$ Denote $M=\text{min}(X_1,X_2,X_3)$. By independence of the $X_i$ ...