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 Probability Old Exam P Forum

#21
07-31-2010, 08:24 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,378

Just a wild guess, since I don't know what the problem is:

Is it the same 2 as in Var(X+Y)=Var(X)+Var(Y)+2*Cov(X,Y)?
#22
07-31-2010, 08:33 PM
 actscience Member Join Date: Jul 2010 Posts: 70

didnt get 2 get cancelled out when we converted 2 (summation of i>J) to (summation of i not equal to j ) ???
#23
05-14-2011, 06:27 PM
 Shaun2357 Member Join Date: May 2011 College: CSUN: B.S in Applied Mathematics Posts: 98

Quote:
 Originally Posted by daaaave I will be teaching an online seminar for Exam 1/P with the Infinite Actuary beginning with the August sitting of the exam. In addition, I will post problems here most weeks along with links to video solutions. The topics of these problems will correspond to the recommended study schedule for the seminar once it gets underway, but before that happens the topics will be fairly arbitrarily. To start, here are some problems on moment generating functions. I've chosen this topic partly because it is relatively late on most people's study schedules and the February sitting is getting close. These questions don't cover everything on the subject, so I will revisit mgf's some time in the future. If anyone has requests for other topics, let me know. ************************************************** 1. Suppose the moment generating function for X is given by $M_X(t)=\frac{4}{(2-t)^2}$ for t<2. Find the variance of X. Link to solution at the end. Numerical answer: Spoiler: Var X=1/2. Intermediate steps may include $E X=1$ and $E\left(X^2\right)=3/2$. ************************************************** 2. Let $Y=2X-3$, where $X$ is a random variable whose moment generating function is $M_X(t)=\exp\left[5e^t-5\right].$ Find $M_Y(t).$ Link to solution at end. Answer: Spoiler: $M_Y(t)=\exp\left[5e^{2t}-5-3t\right]$ ************************************************ 3. Suppose X and Y are random variables whose joint density is given by $f(x,y)=2e^{-x-y}$ for $0 and $f(x,y)=0$ otherwise. Find $M_{X,Y}(t,s)=E e^{tX+sY}$ for $s<1$ and $s+t<2$. Link to solution at end. Answer: Spoiler: $M_{X,Y}(t,s)=\frac{2}{1-s}\cdot \frac{1}{2-s-t}$ ************************************************** ** Video solutions available at the Infinite Actuary

lol, I read this going SWEET then looked at the date...damn
#24
05-14-2011, 06:30 PM
 campbell Mary Pat Campbell SOA AAA Join Date: Nov 2003 Location: NY Studying for duolingo and coursera Favorite beer: Murphy's Irish Stout Posts: 91,425 Blog Entries: 6

Don't worry -- math hasn't changed over the past 4 years.

[also, there are lots of problems at the site - for free, just go over there]
__________________
It's STUMP

#25
10-28-2012, 04:06 AM
 hoanglong252 CAS SOA Join Date: Aug 2011 Studying for Passed P/1 and FM/2 Posts: 9

there are 4 mock exams free on http://www.theinfiniteactuary.com now
#26
03-07-2013, 10:52 AM
 007NewHere Member Non-Actuary Join Date: Feb 2013 Location: Mars Studying for Unknown College: Senior Posts: 805

Hi David,
First of all, thank you for telling me about your free practice exams!!! It is great!!!
I had PM you for one question...then I found this thread...good to post here

I have trouble with #30 (SE1) which I don't really understand the "question"...and I don't understand the last three lines of your solution neither.

Would you please explain it with some details???

#27
03-07-2013, 02:32 PM
 daaaave David Revelle Join Date: Feb 2006 Posts: 3,089

We have 5 variables X_1, X_2, ... X_5 that are uniform on (3, 6). We are ultimately asked to find the probability that the minimum and maximum of our 5 variables are in the interval (4.5 - sqrt{0.15}, 4.5 + sqrt{0.15}).

In order for that to happen, all 5 variables must be in that interval. Each variable individually is in that interval with probability (1/3)*[(4.5+sqrt{0.15}) - (4.5 - sqrt{0.15})] = 2sqrt{0.15}/3. Since the 5 variables are independent, the probability of all 5 being in that interval is [2 sqrt{0.15}/3]^5.
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#28
03-07-2013, 03:33 PM
 007NewHere Member Non-Actuary Join Date: Feb 2013 Location: Mars Studying for Unknown College: Senior Posts: 805

I see...all of 5 X's in that interval...

Thank you!!!
#29
03-08-2013, 08:26 PM
 007NewHere Member Non-Actuary Join Date: Feb 2013 Location: Mars Studying for Unknown College: Senior Posts: 805

Hi David,

I just sent PM to you...according to my personal view of your practice exams...

#30
03-09-2013, 11:37 AM
 007NewHere Member Non-Actuary Join Date: Feb 2013 Location: Mars Studying for Unknown College: Senior Posts: 805

Hi David,

For #12 of SE4, about your solution #1......what is "Y" with Geo(p=0.5)??? Did you suppose that p(1)=0.5 for Y???

Thank you!

 Tags the infinite actuary, tia