Urgently!!! Need to simplify multiple integral

ComplexInfinity

New member

Is it possible to simplify it?
I tried to simplify the numerator of fraction.
My result:
- is it true?

Also my result of denominator for equal functions, when
is:

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
.

royhaas

Full Member
If $$\displaystyle F(x)$$ happens to be the density function of a continuous random variable, then your last integral has the value $$\displaystyle 1/n!$$, which can be seen by a simple substitution.

ComplexInfinity

New member
F(x) is not a density function, F(x) is probability distribution function (0<F(x)<1).

royhaas

Full Member
Same result. In your last expression, let $$\displaystyle y = \int_x ^\infty F(t) dt$$.