Chapter 16 Probability Models

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

Probability Model

Outcome x P(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

Using the Model to Find an Expected Value

• Expected Value: m = E(X) = S (x P(X = x))

Outcome x P(X = x)

Card Payout ($) Probability

Ace of heart 95 1/52

Ace not heart 5 3/52

Heart not Ace 0 12/52

Any other card -5 36/52

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

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