STAB52H3 Lecture Notes - Lecture 8: Sample Space, Binomial Theorem, Joint Probability Distribution
Document Summary
Intuitively, the expected value of a random variable is the average value that the random variable takes on. For example, if half of the time x = 0, and the other half of the time x = 10, then the average value of x is 5. Definition 3. 1. 1 let x be a discrete random variable. Then the expected value (or mean value or mean) of x, written e(x) (or x ), is defined as. Definition 3. 1. 2 let x be a discrete random variable, taking on distinct values x1, x2, , with pi = p(x = xi). Then the expected value of x is given by. Example 3. 1. 2 suppose that p(y = 6) = 1/3, and p(y = 15) = 2/3. Example 3. 1. 6 if x bernoulli( ), then p(x = 1) = and p(x = 0) = 1 , so. Example 3. 1. 6 suppose we have a sample space s and an event a s. we define an indicator function.
