 
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.
