SQRT(RAN#×RAN#) - what is the distribution?

[Csaba Tizedes]

I am working on double (2D) integration routines just for fun on various calculators (implemented two versions (trapezoidal and Simpson's method) on CASIO fx-3650P and on a TI-83 plus - see the video below) and this weekend I want to write a Monte Carlo method for integration (first 1D later 2D).

Unfortunately on CASIOs we have random number generation from 0.000 to 0.999 increased by 0.001, that is 1000 different random numbers equally spaced. My first idea was that, I can increase the number of different random numbers, if I calculate SQRT(RAN#×RAN#). I am sure this will increase the number of numbers, but what about the distribution?

If you have any suggestion about how it can be figure out, please post here. I don't want to make it in EXCEL or write a brute force - thank you!

And my video about a 2D integration on a TI-83 with sightseeing in Budapest, Hungary - check it on YT, the description below the video fullfilled with informations and you can download the 83's program directly:




Csaba