Thread: Two independant and identically distributed uniform distributions

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.

Originally Posted by djones90

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.

1. Note that for , and zero otherwise.

2. Draw the square defined by and and shade the region corresponding to .

3. Then .

I get , NOT ....

my mistake.

Thanks!