Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If we have a random variable $H$, such that

$$ H=B_1G_2\min(1,G_1)+B_2\frac{\min(2,G_1 G_2+G_2)}{n-B_1-B_2}, $$ where $n$ is constant, $G_1$ and $G_2$ are independent lognormal with different parameters, $B_1\sim \operatorname{binom}(n,0.09)$, and $B_2\sim \operatorname{binom}(B_1, 0.02)$, so $B_1$ and $B_2$ are dependent.

It asks for the probability of H being larger than a constant number $c$, say $\operatorname{P}(H>c)$.

I know how to use Monte Carlo directly, but anyone could suggest a faster solution?

Thanks for your time!

share|cite|improve this question
What does "the probability that such thing that bigger" mean? – dfeuer Aug 16 '13 at 0:09
Sorry, just means Pr(H>c), but c can be choosen by any number. – Richard Li Aug 16 '13 at 1:32

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.