Given a function: $$ f(x) = \begin{cases} ax^2 & \text{for } x\in [ -1, 1], \\0 & \text{for } x\notin [-1,1].\end{cases} $$ I am to create a random number generator. I did this by finding the CDF and so I end up with $$X = \sqrt[3]{2F-1}$$ (F being some random variable generated in a spreadsheet, for example)
The problem arises, however, with next tasks:
a) How can we check that this generator generates numbers with a given distribution?
b) Use the generator you found and the knowledge of central limit theorem to create a generator with $N(0,1)$ distribution and test it
(One can use spreadsheet or programming language for the tasks)
So as for the first, can I just generate a lot of data using the generator and then divide the $<max,min>$ into 10 intervals and see if the numbers that fall into them form a bell curve?
As for the latter, If the distribution is to be $N(0,1)$ and the generator from point a) gives me $<-1,1>$, can I just take an absolute value of it and again - divide into intervals, try to see if a bell curve forms?
