Dave Revelle's video problem solving session

[Gandalf]

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)?

[actscience]

didnt get 2 get cancelled out when we converted 2 (summation of i>J) to (summation of i not equal to j ) ???

[Shaun2357]

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.

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1. Suppose the moment generating function for X is given by
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 and .

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2. Let , where is a random variable whose moment generating function is
Find

Link to solution at end. Answer:

Spoiler:

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3. Suppose X and Y are random variables whose joint density is given by
for and otherwise. Find for and .

Link to solution at end. Answer:

Spoiler:

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Video solutions available at the Infinite Actuary

lol, I read this going SWEET then looked at the date...damn

[campbell]

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]

[hoanglong252]

there are 4 mock exams free on http://www.theinfiniteactuary.com now

[007NewHere]

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???

Thank you in advance!

[daaaave]

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.

[007NewHere]

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

Thank you!!!

[007NewHere]

Hi David,

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

Please check your PM. Hope to hear from you soon

[007NewHere]

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!