Can we finally discuss the exam?

[Nonpareil]

Originally Posted by colby2152

Did anyone get questions like these two?

These were not on my test, but for the first one, if you have a joint MGF M(s,t), I think you can find Mx(s) by setting t = 0.

Is the second one asking for a conditional probability? It doesn't seem that way from the description.

[colby2152]

The second question stated... find the probaility that the 70 year old man lived for five years, and then died within the next five years.

[ScubaChris]

Originally Posted by mloiselle

No, that's the thing, it isn't the exact wording. The wording was such that I wasn't absolutely sure if the condition (X>400) applied. Did anyone actually get this question? The wording may have been "a claim was filed." Are claims filed if they are below the deductible?

I definitely had this question and am about 95% sure I put down 3/4.

[Nonpareil]

Originally Posted by colby2152

The second question stated... find the probaility that the 70 year old man lived for five years, and then died within the next five years.

I would interpret that as Pr(5<X<10).

[ultrafilter]

Originally Posted by christian

Is the second one asking for a conditional probability? It doesn't seem that way from the description.

I don't remember the exact wording, but at the time it seemed pretty clear that they were asking for a conditional probability.

[atomic]

Originally Posted by ultrafilter

I got the second one. I set it up as P(X < 10 | X > 5), and got one of the answers given.

Life contingencies notation would be useful. Given the PDF for the lifetime random variable, we compute the survival function s(x), then calculate

.

So for example, if the PDF of age at death for a newborn life is given by f(x) = 1/100, x < 100 (DeMoivre), then the survival function is s(x) = 1 - x/100 and the desired probability is

.

But since the original PDF used in the question has not been mentioned, the above is just a sample calculation.

[smythe]

Yes, I had the question about the 70 year old man. Seemed very straight forward: Find Pr(5<x<10).

[Kazodev]

Originally Posted by atomic

Life contingencies notation would be useful. Given the PDF for the lifetime random variable, we compute the survival function s(x), then calculate

.

So for example, if the PDF of age at death for a newborn life is given by f(x) = 1/100, x < 100 (DeMoivre), then the survival function is s(x) = 1 - x/100 and the desired probability is

.

But since the original PDF used in the question has not been mentioned, the above is just a sample calculation.

isnt' that assuming that f is the pdf of a newborn? I was under the impression from the posts that f is the pdf of a person aged 70?

[mloiselle]

Originally Posted by atomic

Life contingencies notation would be useful. Given the PDF for the lifetime random variable, we compute the survival function s(x), then calculate

.

So for example, if the PDF of age at death for a newborn life is given by f(x) = 1/100, x < 100 (DeMoivre), then the survival function is s(x) = 1 - x/100 and the desired probability is

.
But since the original PDF used in the question has not been mentioned, the above is just a sample calculation.

This result will be the same as:

If is the pdf



Easily seen to be the probability that the lifespan is between 75 and 80 given that it is greater than 70. Could you refer me to a source to find out about the notation you use and why it is convenient. As a beginner, it seems bizarre.

[Kazodev]

It's in chapter 3 of Bowers i.e. define t|u_q_x or something which means the probability of someone aged x dying between x+t and x+t+u. You learn it on course 3/M. So written in prob notation you have P(x+t < X < x+t+u | X > x) = [P(X < x + t + u) - P(X < x + t)]/P(X > x) = [S(x+t) - S(x+t+u)]/S(x)... I think, I haven't taken M