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!

  • $\begingroup$ What does "the probability that such thing that bigger" mean? $\endgroup$ – dfeuer Aug 16 '13 at 0:09
  • $\begingroup$ Sorry, just means Pr(H>c), but c can be choosen by any number. $\endgroup$ – Richard Li Aug 16 '13 at 1:32

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