# Tagged Questions

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### When to use alternate parametrization of Gamma distribution?

In Loss Models, 4th ed., by Klugman et al., the following parametrization is given for the Gamma distribution: $$f(x) = \dfrac{(x/\theta)^{\alpha}e^{-x/\theta}}{x\Gamma(\alpha)}\text{.}$$ When ...
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### What is the pdf of $Z=X/\max(X,Y)$ with $X,Y$ exponentials of lambda parameter?

Given $X,Y$ 2 independent r.v.'s both distributed as $\exp(λ)$, what is the pdf of $Z=X/\max(X,Y)$?
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### Pdf of $Z=(XY)^{1/2}$. with X,Y independent r.v. with the same distribution (iid) [closed]

Let be $X,Y$ two independent random variables having the same distribution (the following is the density of this distribution) $$f(t)= \frac{1}{t^2} \,\,\, \text{for t>1}$$ Calculate the ...
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### pdf vs cdf -random variables-

The following problem is what I am working on. $F(x)=\frac{1}{1+e^{-x}}$ is the cumulative density function defined for all real numbers. Find the probability density function. My understanding ...
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### what is the meaning to evaluate the variance of probability destribution for insurance in general?

what is the meaning to evaluate the variance of probability destribution for insurance in general? What does it do(setting the price, estimate cash reserve or else), also does evaluate the variance ...
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### what is the formal mathematical relationship between the variance and the odds that the gambler who has smaller budget here?

Here is a part of Bob Anderson's answer in my question (Does variance do any good to gambling game makers?) Suppose you had two gamblers who were flipping coins against one another with fair odds ...
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### SOA Exam P Question: Exponential Distribution

Here is an Exam P problem as I have it. That is, it was passed down to me from someone else and I am unsure if the wording is exactly as it was originally posted. I've tried searching for this ...
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### What is a two point support in this lemma?

What is the terminology of two point support in this lemma?
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### Closed form for Exponential Conditional Expected Value & Variance

I am wondering if there is a closed form for finding the expected value or variance for a conditional exponential distribution. For example: $$E(X|x > a)$$ where X is exponential with mean ...