97 reputation
9
bio website
location Minnesota
age 34
visits member for 1 year, 7 months
seen Aug 10 at 2:34

32 Year old female. Mom. Outgoing personality. Z= +2 IQ. Eclectic. SW and LOTR fan. Geek.

Currently studying for my actuarial exams. Exam p/1 (probability) on March 25, 2013. Wish me luck! I taught high school math for a year. I am short of a math degree by 2 courses (differential equations and an advanced elective.) I loved my non-Euclidean geometry class in college but don't remember a thing from it.

Right now I am focusing on honing my calc skills, as well as working intensely on probability in preparation for my Actuarial exam series.

I LOVE explaining solutions to algebra and geometry questions.

Math is cool.


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
May
22
accepted Closed form for Exponential Conditional Expected Value & Variance
May
21
asked Closed form for Exponential Conditional Expected Value & Variance
May
10
awarded  Quorum
May
10
answered SOA/CAS Exam P Question (from previous exam (Nov. '09)): Finding percentiles
May
10
comment Probability of $X^{2} > Y^{3}$ over distribution other than uniform
Thank you for the detailed explanation. Let me see if I can summarize back to you what you said to me... In general, the $X^2>Y^3$ affects the limits of integration, over the support, restricted to this condition. The integrand is whatever the joint pdf is. (If one is lucky- it's easily integrated!) In the special case of the uniform joint pdf, we were able to convert the double integral into the area under the curve, which is why the inequality condition appeared in the integrand, but this is a specific case. The general case is as I first stated. Right? TYVM!
May
8
asked Probability of $X^{2} > Y^{3}$ over distribution other than uniform
Apr
26
comment $P(Y<.5 | X >.5), P(Y>2X), P(.5<X+Y<1.5)$ with Joint probability density function.
... But my arithmetic above was wrong... (added instead of subtracted one of the dozen or so terms.) But I re-did it today with a satisfactory result.
Apr
26
awarded  Commentator
Apr
26
comment $P(Y<.5 | X >.5), P(Y>2X), P(.5<X+Y<1.5)$ with Joint probability density function.
@Dilip - I actually did have it right, you probably just couldn't translate my lazy shorthand. (I didn't know you could use latex in the comments.) Anyway, for posterity: $\int_0^.5 \int_{.5-x}^1 f(x,y)~dydx$ + $\int_.5^1 \int_0^{1.5-x} f(x,y)~dydx$ checks out with wolfies 's answer below. Also, I did the complement as you suggested, and got the same answer.
Apr
24
comment $P(Y<.5 | X >.5), P(Y>2X), P(.5<X+Y<1.5)$ with Joint probability density function.
In that case, is the double integral, int 0 to .5, int (.5-x) to 1 dy dx + int .5 to 1, int 0 to (1.5-x) dy dx? I tried that but second guessed myself. (I got .7266)
Apr
24
awarded  Editor
Apr
24
revised $P(Y<.5 | X >.5), P(Y>2X), P(.5<X+Y<1.5)$ with Joint probability density function.
added part c and more detail for part b
Apr
24
answered $P(Y<.5 | X >.5), P(Y>2X), P(.5<X+Y<1.5)$ with Joint probability density function.
Mar
23
comment Procedure for Max Function with identical random variables
This gets better every time I read it. ;-)
Mar
21
comment How to find limits of integration on a convolution of CRVs
Thanks, everyone! I solved it! I just wanted to say that so others didn't work hard to add thoughtful responses that are not needed. I will edit this answer with more details next week for the benefit of the future struggler... busy studying for now.
Mar
21
comment How to find limits of integration on a convolution of CRVs
I love the diagram method!!! I just don't know how to draw it in this case.
Mar
21
comment How to find limits of integration on a convolution of CRVs
Also, in the case where the two domains are not the same, such as with an exponential and a uniform... I don't understand which to apply and where.
Mar
21
comment How to find limits of integration on a convolution of CRVs
Not to diminish your efforts, but I still don't understand completely. So, there are really two intervals to figure out-- one is the limits of integration and the second is the domain. I assume one comes from the other, but I don't know how to relate them. Also... the infinity case is not clear at all. For a start, how do I split the inequality? Does dividing by -1 make it $-\infty$