why dont you think can be calculated?
And similarly
(i think)
Assuming that integral is correct (check!), can you evaluate it?
Let U and V be independent and identically distributed uniformly on the interval [0,1]. Show that for 0<x<1: .
So far I have worked out the cdf, and hence pdf of . I thought about but a) this doesn't give me the correct answer and b) I don't actually think P(V<U^2) can be calculated.
Could someone give me a hint as to where to go?
Thanks.
Hello !
There's something wrong with your capital letters. It should be small letters within the integrals !
The integral would then rather be :
(since we have put f without any information, the indicator functions are still "in" it, so the boundaries go up to the infinity for v)
And f(u,v) is the joint pdf of U and V, which is the product of their pdf since they're independent.
your right, but i rebel against lower case letters on thursdays
i think its reasonable to put the limits given in the question, its seems like matter of choice whether you define the pdf with an indicator function or over a limited range. (using an indicator function is an interesting idea actually, ive only ever sseen it done this way, but your way is neat).