What is the pdf of the sample maximum?

[Quincy]

Homework Statement

Consider independent random variables X1, X2, X3, and X4 having pdf:

fx(x) = 2x over the interval (0,1)
Give the pdf of the sample maximum V = max{X1,X2,X3,X4}.

The Attempt at a Solution

I can't find ANYTHING about how to solve this in the book, please help!

 

[Klockan3]

One way to start is to try to split the problem into smaller steps, try to solve this one first:

Give the pdf of the sample maximum V = max{X1,X2}

Hint: If X1 is given, what is the probability that X2 is smaller for that value?

 

[Quincy]

Hint: If X1 is given, what is the probability that X2 is smaller for that value?

don't both X1 and X2 have the same pdf?...

 

[Klockan3]

don't both X1 and X2 have the same pdf?...

Yes, and? Having the same pdf doesn't mean that they will always take the same value which is why they are called "independent random variables".