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
Show that X has density $f(x)$.
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probability-theory
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1http://en.wikipedia.org/wiki/Rejection_sampling ? – 2012-11-26