Chapter 4 lecture notes Math 431, Spring 2011 Summary: Chapter 4 lecture notes Math 431, Spring 2011 Instructor: David F. Anderson Chapter 4: Random Variables Section 4.1 Oftentimes, we are not interested in the specific outcome of an experiment. Instead, we are interested in a function of the outcome. Example 1. Consider rolling a fair die twice. S = {(i, j) : i, j {1, . . . , 6}}. Suppose we are interested in computing the sum, i.e. we have placed a bet at a craps table. Let X be the sum. Then X {2, 3, . . . , 12} is random as it depends upon the outcome of the experiment. It is a random variable. We can compute probabilities associated with X. P(X = 2) = P{(1, 1)} = 1/36 P(X = 3) = P{(1, 2), (2, 1)} = 2/36 P(X = 4) = P{(1, 3), (2, 2), (1, 3)} = 3/36. Can write succinctly Sum, i 2 3 4 5 6 . . . 12 P(X = i) 1/36 2/36 3/36 4/36 5/36 · · · 1/36 Example 2. Let X denote the number of successes in n independent trials if the probability of success on each is 0 < p < 1. Collections: Mathematics