Let X1, X2, ..., X, be independent random variables with the random variable X; having density function TA e, 1>0, fx,(x) = 0, I< 0, where v; E {1,2, ...} and i e {1,2, ..., n}. Using any method that we learned from Chapter 6 of our textbook, find the density function for Xị. 1=1

Please answer number 2

Let X and Y be independent random variables. X is N(1,9) and Y is uniform on the interval {--1, 1]. Lat Write down the joint density for (X,Y) o Give the mean and variance of Y c) Give the median of X I dY Give the correlation coefficient p of X and Y

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.