Pls help with this

3. (a) Let 9 (IR) denote the collection of all subsets of real numbers and define 1 if 4EA, 64:5 (R) - [0,00) by 54(A)= 10 if4A. Show that 6, is a probability measure on " (R). (b) State the definition of the independent random variables. (c) Let ? =R, $ =9 (R) and P = 64. Prove that any two random variables X, Y : n - R are independent in the probability space (0, $, P). (d) For any positive integer n 2 1, let f,, : R - K be given by if Ox