1. Chapter 16 Probability Models

2. Who Wants to Play?? $5 to play You draw a card: – if you get an Ace of Hearts, I pay you $100 – if you get any other Ace, I pay you $10 – if you get any other heart, I pay you $5 – if you get any other card, you lose

3. Probability Model OutcomexP(X = x) Random Variable: (X) a variable whose value is based of the outcome of a random event Discrete Random Variable: when there is a finite number of outcomes Continuous Random Variable: when there is an infinite number of outcomes

4. Using the Model to Find an Expected Value Expected Value:  = E(X) =  (x P(X = x)) OutcomexP(X = x) CardPayout ($)Probability Ace of heart951/52 Ace not heart53/52 Heart not Ace012/52 Any other card-536/52

5. Spread First find the deviation (x – μ) Square each deviation Find the variance – the expected value of the deviations Standard Deviation is the square root of the variance

6. Shifting (+/-) and Scaling ( x ) Data Adding or Subtracting a value to each data value will only affect the expected value Multiplying a value by each data value will affect both the expected value and the variance