ZHANG Yan wrote:
>
> Suppose T1,T2...Tn are i.i.d. nonnegative random variable with pdf f(t).
> For two fixed positive value a and b, I have to compute the following
> probability, could you plz give some suggestins? Thanks.
>
> Pr(T1+T2+...Tn < a, T1<b,T2<b...Tn<b) = ?
>
> My solution:
> Pr(T1+T2+...Tn < a, T1<b,T2<b...Tn<b) =
> \int_0^{b} f(t1) \int_0^{b} f(t2) ... \int_0^{a-t1-t2-...-t_{n-1}} f(tn) dtn
> dt_{n-1} ...dt1
>
> But it seems impossible to compute the integral.
>
> --
> ZHANG Yan
> http://www.ntu.edu.sg/home5/pg01308021
I recommend a look at the chapter on probability and statistics
in Mathews & Walker, "Mathematical Methods of Physics". It dis-
cusses something sufficiently like your problem that you can
find the (formal) answer.
--
Julian V. Noble
Professor Emeritus of Physics
[EMAIL PROTECTED]
^^^^^^^^^^^^^^^^^^
http://galileo.phys.virginia.edu/~jvn/
"For there was never yet philosopher that could endure the
toothache patiently."
-- Wm. Shakespeare, Much Ado about Nothing. Act v. Sc. 1.
.
.
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