Deriving Order Statistics

Let Y1, Y2, Y3, and Y4 be four independent random variables, each with density function f(y) = 3 (1-y)^2, 0 < y < 1, and 0 elsewhere. Derive the distribution function and the density function of Y1 and Y4.

**Note: Although this is an ordered statistics problem, I am to derive and not plug into the ordered statistics formula. Further, I am ttying to derive the distribution of the first order statistic and the last order statistic, not their joint distribution.

Re: Deriving Order Statistics

Hey bullmoose97.

Are you trying to find a minimum or a maximum distribution?

Re: Deriving Order Statistics

Hi Chiro,

I'm actually trying to find both the max and min distributions.

Thanks!

Re: Deriving Order Statistics

The first thing to do is write out the cumulative distribution function of the maximum. (Hint: If something is a maximum then all random variables are less than it and the product of CDFs is for the CDF of independent distributions).