# Tagged Questions

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### Proving $E_{\theta}[T(X)] = \frac{\psi'(\theta)}{\eta'(\theta)}$

I'm trying to understand how to prove the following theorem: Let $\{P_{\theta}, \theta \in \Theta\}$ be a family of distributions in the one parameter exponential family with density (pmf) ...
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### Derive the PDF of the log-normal distribution?

If $X \sim N(0,1)$ and $Y = e^X$, find the PDF of $Y$ using the two methods: (i) Find the CDF of of $Y$ and then differentiate. Use the notation $\Phi(x)$ and $\phi(x)$ for the CDF and PDF of $X$ ...
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### Expected value of minimum of exponentials

I am not sure of the following. I have $(i-1)$ exponential random variables with rates $\theta$ and $\mu$ and I want the expected value that the particular $\mu$ random variable is the minimum. Think ...
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### Non-trivial solution for $2*a^k = b^k + c^k$

I have a data set where I want its median to be the arithmetic average of maximum and minimum by multiplying every value with a factor $k$ and then applying the exponential function. This leads to the ...
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### How do I find the mean with this exponential?

p(y) = c/y^4 I need to find the "mean & variance" of this exponential density function. Some pointers or thoughts that would explain would be most helpful. ...