1. If a random sample of size 2 is taken from a distribution having p.d.f. j(x) = 2(1 - x), 0 <>x <>1, zero elsewhere, compute the probability that one sample observation is at least twice as large as the other.
2. Let Y1 Y2 Y3 denote the order statistics of a random sample of size 3 from a distribution with p.d.f. f(x) = 1, 0 x 1, zero elsewhere. Let Z = (Yi + Y3)/2 be the midrange of the sample. Find the p.d.f. of Z.