Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $U$ be a Standard Uniform random variable. Show all the steps required to generate a continuous random variable with the density $f(x) = 1.5x^2$, $-1 < x < 1$.

I'm not looking for exact answers as much as proper solutions for future reference. Thanks!

share|cite|improve this question
up vote 3 down vote accepted

Denote new random variable as V and its distribution function as F(x). Then:

F(x)=(x^3+1)/2=G( G` (F(x) ) )=G( (x^3+1)/2 )=P( U <= (x^3+1)/2 ) =P( 2U-1 <= x^3 )=P( (2U-1)^(1/3) <= x ). So, (2*U-1)^(1/3) is that random variable you need.

(As G`(x) I denote inverse function for G(x). G(x) is distribution function for U)

share|cite|improve this answer

Hint: You want to solve $F(X) = U$, where $F$ is the cumulative distribution function.

share|cite|improve this answer
So would I just integrate 1.5x^2 between -1 and 1 for the answer? – jrquick Dec 3 '12 at 20:21
No, integrate between $-1$ and $X$. – Robert Israel Dec 3 '12 at 20:43

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.