1
$\begingroup$

Let $$f(x)=60x^3(1-x)^2,\quad 0

Let $U_1,U_2,...$ and $V_1,V_2,...$ i.i.d. random variables with distribution $U(0,1)$. We build a random variable X as follows: $$U_1\leq60V_1^3(1-V_1)^2/60=V_1^3(1-V_1)^2,$$ If thats not true, we try with $U_2$ and $V_2$:

if $$U_2\leq V_2^3(1-V_2)^2,$$ then $X=V_2$.

If not, we try with $U_3$ and $V_3$, etc. Show that X has density $f(x)$.

It's from an old probability test and a have no idea how to start, could use some hints

  • 1
    http://en.wikipedia.org/wiki/Rejection_sampling ?2012-11-26

1 Answers 1