You want to derive the density function of a maximum, where U1, ..., U10 follows an uniform distribution.
and the density function can be obtained by calculating its derivative.
Lets say I have 10 random numbers U(0,1). I have a variable called B that is defined as B=max{U1,U2,...U10}
I want help to prove that the density function of B is given by;
f_B(r) = 10*r^9 where r is in the interval [0,1]
How can I show this?
the idea is right, but the U's are part of B, not the argument.
using independence...
Since the cummulative distribution of a U(0,1) is when 0<r<1.
NOW differentiate wrt r, which is a Beta by the way.