I would like to make multi-variate integration over 9 variables (x11, x12, x13, x21, x22, x23, x31, x32, x33) in order to calculate the probability of a given event.
The output of the simpleWeightedSum method is a Vector(3,t), giving the mean of the rows of the matrix X. The event which I would like to "measure" is that the first element of the output vector is higher than the two other elements.
The xij elements are iid variables with uniform distribution between 0 and 1. I would expect 1/3 as result of the integration (giving the probability when the sum of the first row is higher than the sum of the second or third row)
My problem is that I can't make Maple to calculate the integration. I try numeric integration, because I will have more complex functions than simpleWeightedSum.
For some reasons I could not insert the contents, just the link of my uploaded mw file, please look on that.
I tried the followings:
Int(myFunc(x11, ... x33) , [x11=0..1 , ... , x33=0..1], epsilon=0.0001,digits=10); evalf(%)
This did not finish, I aborted its run
Int(myFunc(x11, ... x33) , [x11=0..1 , ... , x33=0..1], method=_MonteCarlo, epsilon=Epsilon,digits=numOfDigits); evalf(%)
This one finished but generates different results by increasing Epsion and numOfDigits. I expected that as Epsilon or numOfDigits increases, the result will approach some values, but this is not the case. I don't know which numbes to set for epsilon and digits in case of the _MonteCarlo method?
Is it possible to calculate this integration?
Can we set the number of points used in MonteCarlo?
Why Montecarlo is giving alternating and different results by increasing digits and epsilon?