Consider a random sample Y... In of a normal distribution with mean u and variance ?. Let the following variables be : X = Y- M ; x , = You : X3 = (n - 1 ) s' ; X x = X - + X3 Ca ) Determine the distribution of each of the variables X ...X , specifying their parameters . (b) Let n = 10 . With R, calculate the following probabilities : i ) p ( X L 1 966 1: ) P ( X , > 3 . 45 ) in ) P ( X 3 > 8 - 35 ( V ) P ( X 4 > 12. 35