Let Y1, Y2, . . . , Yn be independent and identically distributed with following probability density function f(y) = 4(1 - y) ^3, 0 < y < 1 f(y)= 0 otherwise
(a) Determine the probability density function of Y(1) = min(Y1, . . . , Yn).
(b) Determine the probability that Y(1) is less than 0.1.
(c) Determine the expected value of Y(1). (Hint: beta distribution).
(d) Find the variance of Y(1). (Hint: beta distribution).