Let U and V be independent and identically distributed uniformly on the interval [0, 1].
Show that for 0<x<1;
P(x<V<U^2)=1/3 - x + (2/3)*x^3
and hence write down the density of V conditional on the event that V<U^2.
Let U and V be independent and identically distributed uniformly on the interval [0, 1].
Show that for 0<x<1;
P(x<V<U^2)=1/3 - x + (2/3)*x^3
and hence write down the density of V conditional on the event that V<U^2.