1
vote
2answers
41 views

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 ...
4
votes
1answer
58 views

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 $Z=X/\max(X,Y)$?
0
votes
2answers
58 views

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 ...
0
votes
2answers
22 views

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 ...
0
votes
1answer
57 views

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 ...
1
vote
1answer
66 views

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 ...
2
votes
1answer
161 views

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 ...
0
votes
2answers
70 views

What is a two point support in this lemma?

What is the terminology of two point support in this lemma?
1
vote
2answers
271 views

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 ...
1
vote
1answer
140 views

$e^{F(x,y)}$ Type Multi-variable Exponential Integrals

I am sure all you integration buffs can do this faster than I can type it. Your help with a quick explanation and solution is appreciated. $$F _{XY} = \int_0^\infty\int_0^\infty xye^{-\frac{x^2 + ...
1
vote
1answer
230 views

Stuck on solving for x in exponential to find variance

The problem seems simple: Let X be an exponential random variable such that $P(X \le 2) = 2P(X > 4)$. Find the variance of X. Easy, right? $ P(x \le 2) = 1 - e^{-2\lambda} $ and $ P(x > 4) = ...
1
vote
2answers
171 views

Where is the logic with this trinomial probability?

I am studying for Exam P to take in a few hours so I'd appreciate very much if someone got to me befoe I left. The problem says that we have three categories of risk, high, medium and low risk. The ...
1
vote
2answers
131 views

Are waiting times always going to be exponentially distributed?

I'm studying for CAS/SOA Exam P/1 and a question I have here is: We have a portfolio of $20$ insurance policies. The number of claims per policy in a $3$-month period has a Poisson distribution ...
1
vote
1answer
690 views

What does it mean that the probability density function is proportional to a function?

I'm studying for SOA/CAS Exam P and I have a problem that says that $X$ is a continuous and positive random variable whose probability density function is proportional to: $$\frac{1}{(1+x)^5}$$ Where ...
0
votes
3answers
373 views

SOA/CAS Exam P Question (from previous exam (Nov. '09)): Finding percentiles

So this question comes from SOA/CAS Exam P of November 2009, I'm not sure why the solution is the way it is. The question says this: An insurance company sells an auto insurance policy that ...