Krzysio's Weekly Practice Problems for M/3

[krzysio]

It is posted by Dr. Ewa Kubicka at:
http://www.math.louisville.edu/~ewa/...m-04-01-06.pdf
Yours,
Krzys'

[silverfox]

Welcome to our newest member, Ewa Kubicka

[krzysio]

It is posted at:
http://www.math.ilstu.edu/krzysio/KO...cise-4-8-6.pdf

Yours,
Krzys'

[krzysio]

Originally Posted by Searching.

I haven't worked through the entire problem, but for the first integral, the integrand of which is e^(-.15t)*.05t, you get 1-e^(-30)/3. It appears that you worked the integral as if the integrand were e^(-.15t)*.05 and then wrote .15*20 as 30 and not 3. It seems like the answer will be quite different then, but perhaps I have missed something.

Edit: Working the problem by adding individual term insurances of 2 for death by accident and 1 for death by other means, I get (after integration by parts):

2*.05*[(1-e^-3)/.15^2 - (20e^-3)/.15]=3.559

Can you confirm this, Professor K, or am I just way off? Thanks.

I have posted a longer explanation of what I am doing in the solution now:
http://www.math.ilstu.edu/krzysio/KO...cise-4-8-6.pdf
You do need to account for survival from both causes until death from a cause, so I do not think your solution works. Take a look at a more detailed solution I posted, it shows all steps in the integral.
Yours,
Krzys'

[carrytheCrøss]

Thank you very much; I now see what I was doing wrong. I was using e^(-.015t) and not e^(-.015t^2/2) as the survival probability in the integrand.

Thanks for taking the time as always.

[Ewa Kubicka]

It is posted at:
http://www.math.louisville.edu/~ewa/...m-04-15-06.pdf
Happy solving,
Ewa Kubicka

[carrytheCrøss]

Originally Posted by krzysio

I have posted a longer explanation of what I am doing in the solution now:
http://www.math.ilstu.edu/krzysio/KO...cise-4-8-6.pdf
You do need to account for survival from both causes until death from a cause, so I do not think your solution works. Take a look at a more detailed solution I posted, it shows all steps in the integral.
Yours,
Krzys'

Strangely enough, the CAS used this as Question 18 of CAS 3, Fall '05, making no modifications besides changing the order the information was presented. I realized this as I was working the exam as practice last night. Indeed, it definitely pays to look at questions from years past.

[Ewa Kubicka]

The corrected version of the problem is posted at:
http://www.math.louisville.edu/~ewa/...m-04-01-06.pdf.

Ewa

[krzysio]

It is posted at:
http://www.math.ilstu.edu/krzysio/KO...ise-4-22-6.pdf

Yours,
Krzys'

[krzysio]

Originally Posted by Searching.

Strangely enough, the CAS used this as Question 18 of CAS 3, Fall '05, making no modifications besides changing the order the information was presented. I realized this as I was working the exam as practice last night. Indeed, it definitely pays to look at questions from years past.

Indeed. It definitely makes sense to do a lot of problems from past exams, I strongly advocate that.

I was actually not aware of this repeat of the SOA exam on the CAS exam, but I appreciate your insight -- and I do have a nearly identical solution to the CAS problem in my manual. This is a good exercise, anyway.

Yours,
Krzys'