Expected Value of Y = max (X1, X2, X3, .... , Xn)

#1
I'm having a hard time figuring out what the expected value of Y = max(X1, X2, X3, ... , Xn) with pdf (x;θ) = 2x/θ^2. So it is the nth value of order statistics Y1<Y2<Y3.....<Yn. Does anyone know?
 

BGM

TS Contributor
#2
First you need to find out the CDF (and thus the pdf) of \( Y \), then you can find out the expectation.

The CDF can be find out by the definition of maximum and CDF respectively, and this is a typical exercise.