1
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1answer
38 views

Proof of $\text{TVaR}_p(X)$ and $\text{VaR}_{u}(X)$ relationship

From Loss Models, 4th ed., by Klugman et al.: Definition. Let $X$ denote a loss random variable. The Value-at-Risk of $X$ at the $100p$% level, denoted $\text{VaR}_{p}(X)$ or $\pi_p$, is the ...
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2answers
27 views

Definition of Percentile (undefined notation)?

From Loss Models, 4th ed., by Klugman et al.: Definition 3.6 The $100p^{\text{th}}$ percentile of a random variable is any value $\pi_p$ such that $F\left(\pi_{p^{-}}\right) \leq p \leq ...
1
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0answers
62 views

Probability of remaining lifetime using force of mortality

I've been stuck on this question for the past half hour and still have no idea how to solve it... I don't think it's supposed to be very difficult but I'm struggling: There are two independent live ...
1
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3answers
40 views

Bayesian Statistics

Question: Given $N$, $X$ is distributed as $\mathrm{B}(N,\theta)$. Derive the unconditional distribution of X assuming N is distributed as $P(\lambda)$. This is what I have tried so far: $$x|N \sim ...
-1
votes
1answer
49 views

poisson and discrete distribution

Business failures are due to three mutually exclusive risks: market risk, credit risk, and operation risk, which account for 20%, 30%, and 50%, respectively, of all business failures. Suppose the ...
0
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1answer
24 views

Poisson Process Basic Question

The sum of independent interarrival times for the poisson process is a gamma random variable. in general does the sum of exponentials have to be independent to sum to gamma? also this would produce ...
0
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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 ...
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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 ...
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1answer
86 views

When does variance fail to meet its purpose in mathematical statistics? [closed]

It have shown in a lot of both math and statistics book, however, When the books define the variance, it doesn't give much attention to math based theoretical background, i wonder if some formula that ...
2
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1answer
90 views

Variable substitution in probability

In modeling the number of claims filed by an individual under an automobile policy during a three-year period, an actuary makes the simplifying assumption that for all integers $n \ge 0$, ...
0
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1answer
71 views

How to calculate $\Pr[\max(X,Y)<4]$?

Suppose the joint PDF of X,Y is $f(x,y)=1/40$ and $0 < x < 5$ and $0 < y < 8$. How to calculate $\Pr[\max(X,Y)<4]$?
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1answer
97 views

What is some application of variance in actuarial science/insurance risk?

What is some application of variance in actuarial science/insurance risk? I learn that a lot of applied math book of actuarial science have variance of probability distribution frequently. Don't ...
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2answers
424 views

Finding moment generating function from piecewise CDF

I am stuck on this problem: I am given the CDF, and unless there is a shortcut I am not remembering, I need to find the PDF before I can get the moment generating function and solve the problem. ...
1
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2answers
216 views

Probability of being within one standard deviation of mean given only a moment generating function

I am trying to figure out how to approach this: For starters, I calculated M'(0) and M"(0), which allowed me to find the mean and variance. I got 2 for the mean and 1.6 for the variance. But now, ...
80
votes
9answers
22k views

How often does it happen that the oldest person alive dies?

Today, we are brought the sad news that Europe's oldest woman died. A little over a week ago the oldest person in the U.S. unfortunately died. Yesterday, the Netherlands' oldest man died peacefully. ...
3
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3answers
2k views

Masters in Actuarial Science

I am applying to a grad school for the Masters in Actuarial Science. Now i am getting cold feet. I do love math, i was always good in math (not excellent or a genius). Did all adv. calculus classes ...