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.