2. Minimum and Average In this exercise you will discover properties of the sample minimum and the sample average of i.i.d. samples taken from two well-known distributions. If necessary, you can leave answers in terms of the standard normal cdf (I). (a) Let U1, U2, , U\" be i.i.d. uniform (O, 1) random variables and let X\" = min{U1 , U2, , UH}. Find the survival function of X" and hence find the density of X n. (b) Let T1, Tz, , Tn be i.i.d. exponential (A) random variables and let Y\" = min{T1, T2, , Tn}. Find the survival function of Y\" and hence identify the distribution of K, as one of the famous ones; remember to provide the relevant parameters. (e) Let U1, U2, , U,1 be i.i.d. uniform (0, 1) random variables and let V = i 2;] U,-. For large it, find an approximation to the survival function of V\". (cl) Let T1, T2, , Tn be i.i.d. exponential (A) random variables and let M = % 2:1 '1}. For large n, find an approximation to the survival function of IV\