We choose a number from the set {10, 11, 12, . . . , 99} uniformly at random.

(a) Let X be the first digit and Y the second digit of the chosen number. Show that X and Y are independent random variables.

(b) Let X be the first digit of the chosen number and Z the sum of the two digits. Show that X and Z are not independent.

This is all the data. The questions are about independency. the set of numbers go from 10-99. X stands for the first number and Y the second number. So for example, the number 12, X = 1 and Y =2.