Most discrete random variables can take on a finite number of values. Let X = the number of rolls of two dice necessary until doubles (the same number on each die) first appears. The possible values for this discrete random variable (called the geometric) are 1, 2, 3, 4, 5, 6, 7, and so on, still separate values (and discrete) but now an infinite number of them.
a. Using intersections of independent events, explain why P(1) = 1/6, P(2) = (5/6)(1/6), and P(3) = (5/6)2(1/6).
b. Find P(4), and explain how to find P (x) for an arbitrary positive integer x .