# Questions tagged [gamma-distribution]

For problems that are related to gamma-family probability distributions.

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### What is the relationship between poisson, gamma, and exponential distribution?

I'm having a hard time understanding the intuitive relationship between these three distributions. I thought that poisson is what you get when you sum n number of exponentially distributed variables, ...
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### Problem with the expectation of a maximum of independent gamma distributed random variables

Having a problem with the expectation of the maximum among $n$ independent random variables $X_1, X_2 \dots X_n$ all ~ the same class of distributions but not necessarily the same mean and other ...
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### Invert a somewhat tricky characteristic function to find density function

I am interested in find the probability density function corresponding to the characteristic function $\phi(t) = \left(\frac{1 - i b t}{1 - i t}\right)^c$ where $c > 1$ and and $0< b < 1$. ...
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### Let $X|Y = y\sim\text{Poisson}(y)$ and $Y\sim\text{Gamma}(\alpha, \lambda)$. Find $f_X(x)$.

Question: Let $X|Y = y\sim\text{Poisson}(y)$ and $Y\sim\text{Gamma}(\alpha, \lambda)$. Find join density $f_{X,Y}(x,y)$ and find the probability density function of $X$ (simplify until there are no ...
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### chi squared distribution of independent normal distributions that are not standard normal

I've been working on the following problem. I'm a bit confused about some of the specifics of how to arrive at the correct answer. I hope someone here could point me in the right direction: A dart ...
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### Unit Measure Axiom for the Gamma Distribution

I'm studying basic probability and in my lecture notes, it shows how the Gamma function results from the convolution of two exponential random variables. To introduce the gamma function it shows that ...
### Evaluate $\lim\limits_{\alpha \to \infty} e^{-\frac{t}{\sqrt{\alpha}}}(1-\frac{t}{\sqrt{\alpha}})^{-\alpha}$ [duplicate]
How does one show $$\lim_{\alpha \to \infty} e^{-t\sqrt{\alpha}}\left(1-\frac{t}{\sqrt{\alpha}}\right)^{-\alpha} = e^{t^2 / 2}?$$ Not homework, this is from this proof that the gamma distribution ...