0
$\begingroup$

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!

$\endgroup$
3
$\begingroup$

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)

$\endgroup$
0
$\begingroup$

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

$\endgroup$
2
  • $\begingroup$ So would I just integrate 1.5x^2 between -1 and 1 for the answer? $\endgroup$ – Jeremy Quick Dec 3 '12 at 20:21
  • $\begingroup$ No, integrate between $-1$ and $X$. $\endgroup$ – Robert Israel Dec 3 '12 at 20:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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