Chapter 16

1. Chapter 16 Random Variables

2. 2 Types of Random Variables • Discrete Random Variable – can be listed or counted. • Number of students in a class • Number of cars owned • Number of defective bulbs in a package of 10 • Continuous Random Variable – the variable can assume any value within a range of values (usually measurements). • Height • Weight • Time

3. Probability Model • When modeling data in previous chapters we called it a distribution (actual sample data have a distribution). • Random variables have a probability model—these models describe what we expect to happen (in theory); they do not provide us with actual data.

4. Probability Model • The model’s mean is the expected value of the variable: • Written µ or E(X)…but not x-bar. • The model’s variance is • Var(X) or σ2…not s2 • A key thing to remember from this chapter: • Variances add!—the variance of the sum of two independent random variables is the sum of their variances.

5. Expected Value Example • A game…A player pays $5 to play and draws a card from the deck. If he draws the ace of hearts, he wins $100. For any other ace, he receives $10, and for any heart he gets $5. If he draw anything else, he loses. • Would anyone be willing to play this game? • What if the top prize was $200?

6. Solution • There are 4 payouts, $95, $5, $0, and -$5. • The probabilities are 1/52, 3/52, 12/52, and 36/52, respectively. • Calculating the E(X) gives you -$1.35. Your expected value is negative… • What about with a $200 prize?

7. Assignment • Design a game of chance • Create the rules • List the payoffs • Set the cost of playing • The objective is to make a game that looks appealing so many people would be eager to play, but whose expected value and standard deviation make it likely that the person running the game would realize a profit.