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ComplexInfinity
03-30-2008, 06:36 AM
Please, help:
http://lib.mexmat.ru/math/dac8e674331258c2ddfa93fb1ebe2bf582.gif
Is it possible to simplify it?
I tried to simplify the numerator of fraction.
My result:
http://lib.mexmat.ru/math/32a3db3de94e6f10e4050b635ad223a982.gif - is it true?

Also my result of denominator for equal functions, when http://lib.mexmat.ru/math/4ee26c758444c4ace5202df89c85c64f82.gif is:
http://lib.mexmat.ru/math/4e1a59a1528599eed3d3bad78631c5e282.gif
but I'm not sure ...
I want to solve this problem for case, when all these functions are different. Help ...
I'm considering the case when http://lib.mexmat.ru/math/39889726e9c0a9824cfb5cc2faf2d7d982.gif.

Thanks in advance.

royhaas
03-30-2008, 07:00 AM
If F(x) happens to be the density function of a continuous random variable, then your last integral has the value 1/n!, which can be seen by a simple substitution.

ComplexInfinity
03-30-2008, 07:22 AM
F(x) is not a density function, F(x) is probability distribution function (0<F(x)<1).

royhaas
03-30-2008, 06:00 PM
Same result. In your last expression, let y = \int_x ^\infty F(t) dt.