suppose that f(y) = { 3y^2, 0<=y<=1                                      0, otherwise a) verify that f(y) is a valid probability density function.b) Determine the expected value of Yc) Determine the variance of Yd) Find the cumulative distribution function of Ye) Determine the probability that Y does not exceed 1/2

b) Let Y,,Y2, .. , Yn denote a random sample from N(0,0) distribution with probability density function: f(y;8) = e V2n0 i) Show that f(y; 0) belongs to the 1-parameter exponential family. ii) What is the complete sufficient statistic for 0? Justify your answer. iii) Show whether or not, the maximum likelihood estimator is an unbiased estimator of 0. iv) Does the estimator attains the minimum variance unbiased estimator of 0.