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# Thread: TIPS and TIME SAVERS for Exam P

1. ## TIPS and TIME SAVERS for Exam P

If you have any shortcuts to save time during the test, please share. Here are a few of mine:

1)

This one saves from messy integration by parts, which I discovered on accident...

If a policy limit L is applied to an EXPONENTIAL distribution, the new mean is the old mean (theta) multiplied by the probability that X<L.

If a deductible D is applied to an exponential distribution, the new mean is the old mean multiplied by the probability that X>D.

These formulas, shown below, can also be used to find the deductibles or limits needed to alter the means.

Let u=original mean (theta); v=new mean after L or D is enforced...

v=u(1-e^(-L/x))

v=u(e^(-D/x))

Thus if we want the expected claim payment to be 20% less than the \$500 mean damage distributed exponentially by adding either a limit or deductible...

New expected claim payment = 400

400 = 500(1-e^(-L/500))
Thus L = \$804.72

OR

400 = 500(e^(-D/500)
Thus D = \$111.57

+++++++++++++++++

2)

If X and Y follow independent exponential distributions with means 2 and 3, what is the probability Y<X? (And for other multivariate distributions...)

If the answers are separated by more than 3% or so, instead of double integrating the joint density function, a quick glance at the normal distribution table seems appropriate, no?

(I'm assuming that this table is the one and only information that will be provided during the test???? Anyone know?)

2. Originally Posted by qok
(I'm assuming that this table is the one and only information that will be provided during the test???? Anyone know?)
Yes it is :geek:

3. Im thinking these really don't seem like much of a shortcut....they are just obviously what you are doing when you find the E[X] if I am understanding correctly.........

A short-cut could be using the tabular method when integrating....
Or knowing how to use the survival function to find expected value....
Or memorizing thoses properties for distribution functions

4. I don't remember doing too much hard integration when I took P. A real time-saver is memorizing the main distributions, their MGF's, means, and variances. That way if your given an MGF or a distribution, you need to do barely any work to get a variance, stdev, or mean.

5. Originally Posted by djerry81
Im thinking these really don't seem like much of a shortcut....they are just obviously what you are doing when you find the E[X] if I am understanding correctly.........
Well, I thought this only worked for exponential because of the memoryless property. Integrating f(x)(x-d) would not work otherwise and for the limit, there's the need to consider that for x>L that E[X] incorporates the value L for L to infinity, which doesn't seem part of the survival function. I've seen these problems solved three times by a textbook which always uses a full page of integrating f(x)(x-d) or f(x)*x.

Originally Posted by djerry81
A short-cut could be using the tabular method when integrating.... Or knowing how to use the survival function to find expected value....
Thanks for the survival rule tip; I just read it. I bought the ASM study manual for the practice exams, but now I'll have to read the first 100 pages too to learn the things my other manual never mentioned.

I'm guessing the tabular method in the ASM study manual too?

6. Originally Posted by qok
I'm guessing the tabular method in the ASM study manual too?
Sorry, but no, I am not a fan of the tabular method of integration by parts, because you really should use integation by parts of the first exam very, very rarely. If you are doing integration by parts on exam P, you probably failed to memorize something you should memorize. If you are doing integration by parts on exam MLC, you definitely failed to memorize something you should memorize. The mindset of examiners is the same, really. For example, you might be doing integration by parts because you were too lazy to memorize the gamma function. But in the minds of examiners, a real actuary knows the gamma function.

Yours,
Krzys'

7. Originally Posted by krzysio
Sorry, but no, I am not a fan of the tabular method of integration by parts, because you really should use integation by parts of the first exam very, very rarely. If you are doing integration by parts on exam P, you probably failed to memorize something you should memorize. If you are doing integration by parts on exam MLC, you definitely failed to memorize something you should memorize. The mindset of examiners is the same, really. For example, you might be doing integration by parts because you were too lazy to memorize the gamma function. But in the minds of examiners, a real actuary knows the gamma function.

Yours,
Krzys'
yea the gamma function this tool is so nifty......

8. Basically You won't need integration by parts because you should know the gamma function

9. Originally Posted by qok
Thanks for the survival rule tip; I just read it. I bought the ASM study manual for the practice exams, but now I'll have to read the first 100 pages too to learn the things my other manual never mentioned.
:smiloe: Hi qok. I was wondering if that other manual was the ACTEX. What do you think about the ASM study manual? I'll be sitting for Exam P in November and so I need to purchase a study manual ASAP. Any suggestions or recommendations?

Thanks

10. Originally Posted by krzysio
because you really should use integation by parts of the first exam very, very rarely. If you are doing integration by parts on exam P, you probably failed to memorize something you should memorize.
I used integration by parts constantly on P. Why? Because it's easy, and I prefer to know one general technique rather than memorize a whole ton of special cases. Come on, it takes two lines and 60 seconds. And, it has the definite benefit that you can check your work.

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