Thread: Random Number Generation

I was asked to show all steps required to generate certain functions, distributions, etc. using only the fact that I am given a random u~unif(0,1)
On two of them I had a slight problem/question, so here they are:

A continuous random variable with pdf f(x) = 1.5x^2, -1=< x =< 1
I calculated the cumulative function F(x) by integrating 1.5x^2 from -1 to x, which gave me .5x^3 + .5, then set that equal to u and solved for x. Is this the correct process? What I'm most worried about is whether or not I integrated with the right bounds, or where the bounds on x come into play elsewhere

A continuous random variable with pdf f(x) = (1/12)x^(1/3) on 0 =< x =< 8
I integrated from 0 to x to get (3/48)x^(4/3), but once again I have no idea if this is correct. Where would the 8 be used?

Thanks for any help!!

Originally Posted by mistykz

I was asked to show all steps required to generate certain functions, distributions, etc. using only the fact that I am given a random u~unif(0,1)
On two of them I had a slight problem/question, so here they are:

A continuous random variable with pdf f(x) = 1.5x^2, -1=< x =< 1
I calculated the cumulative function F(x) by integrating 1.5x^2 from -1 to x, which gave me .5x^3 + .5, then set that equal to u and solved for x. Is this the correct process? What I'm most worried about is whether or not I integrated with the right bounds, or where the bounds on x come into play elsewhere

A continuous random variable with pdf f(x) = (1/12)x^(1/3) on 0 =< x =< 8
I integrated from 0 to x to get (3/48)x^(4/3), but once again I have no idea if this is correct. Where would the 8 be used?

Thanks for any help!!

Both problems look correct to me.

The 8 does not explicitly appear in your calculations for the second part, but if you did your algebra correctly the pseudo-random numbers you generate will automatically turn out to be in the range from 0 to 8.

Alright, thanks!