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.

Hey bullmoose97.

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

Hi Chiro,

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

Thanks!

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).