Re: [Maxima-discuss] "distrib" package

[Henry B. <hb...@pi...>]

Since I'm so dense, what would be the probability when the group has size _one_;
i.e., choose a from the top 1% of A and choose b from the top 1% of B; what is
the probability that a beats b ?

BTW, I tried "laplace" and "ilt", but they didn't work.  More precisely, "laplace"
seemed to work ok, but "ilt" failed miserably.

I also noticed that integrate(foo(x)*unit_step(x),x,minf,inf) isn't smart enough
to simplify to integrate(foo(x),x,0,inf).

At 11:00 AM 9/3/2014, Robert Dodier wrote:
>On 2014-09-03, Henry Baker <hb...@pi...> wrote:
>
>> On a particular Olympic sport, the abilities of any individual
>> in a population is normally distributed.
>>
>> Thus, for country A, with population Ap, mean Am, variance Av,
>> the abilities of the individuals follow a normal distribution.
>>
>> Clearly, each country will choose from the upper tail of the
>> distribution -- its highest 1%, for example.
>>
>> What is the probability that a 1% athlete from A will beat a 1%
>> athlete from B, given the population, mean and variance of each country ?
>
>We are looking for P(ability(A) - ability(B) > 0) where ability(A)
>and ability(B) are Gaussian tail distributions. That is, not the
>entire bump (i.e. national population) but just the 1% who
>are sent to the games. I think Maxima can figure out the density of
>ability(A) - ability(B) exactly, but one must be careful with the
>limits of integration in the convolution since we are working with
>just the tails. Note sure if Maxima can then compute P(diff > 0)
>since that requires another integration.
>
>I worked on a related problem recently. For the record:
>http://maxima-solved.blogspot.com/2014/06/probability-density-of-sum-of-gamma-and.html
>
>> Now, suppose that we have a _group sport_ which requires a small
>> number (k) athletes, and that the performance of each country is
>> additive -- e.g., the gymnastics "team" medal, where the team is
>> of size k.
>>
>> Now, what is the probability that country A will beat country B ?
>
>Well, for k larger than a few, the group ability is nearly Gaussian
>even though the individual abilities are very non-Gaussian (via
>central limit theorem). So one can come up with an approximation
>more easily in the group case.
>
>Sounds like fun -- good luck.
>
>Robert Dodier