# EXPECTED VALUE RULES 1. This sequence states the rules for manipulating expected values. First, the additive rule. The expected value of the sum of two.

## Presentation on theme: "EXPECTED VALUE RULES 1. This sequence states the rules for manipulating expected values. First, the additive rule. The expected value of the sum of two."— Presentation transcript:

EXPECTED VALUE RULES 1. This sequence states the rules for manipulating expected values. First, the additive rule. The expected value of the sum of two random variables is the sum of their expected values. 1

EXPECTED VALUE RULES 1. Here the sum consists of three variables. But the rule generalizes to any number. 2

EXPECTED VALUE RULES 1. 2. The second rule is the multiplicative rule. The expected value of a variable that has been multiplied by a constant) is equal to the constant multiplied by the expected value of the variable. 3

EXPECTED VALUE RULES 1. 2. Example:
For example, the expected value of 3X is three times the expected value of X. 4

EXPECTED VALUE RULES 1. 2. 3. Finally, the expected value of a constant is just the constant. Of course this is obvious. 5

EXPECTED VALUE RULES 1. 2. 3. As an exercise, we will use the rules to simplify the expected value of an expression. Suppose that we are interested in the expected value of a variable Y, where Y = b1 + b2X. 6

EXPECTED VALUE RULES 1. 2. 3. We use the first rule to break up the expected value into its two components. 7

EXPECTED VALUE RULES 1. 2. 3. Then we use the second rule to replace E(b2X) by b2E(X) and the third rule to simplify E(b1) to just b1. This is as far as we can go in this example. 8