Independent Events

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Independent Events

• Raul Cruz-Cano
• MATH 453 Spring 2008

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Announcements

• Thursday Homework is due (there are few
  opportunities to get points)
• Microsoft Talk Free points (sign sheet) and send
  me resume

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Independent Events

• The rule apply even for more than two events
• A Head (coin toss)
• B 6 (die)
• C Head (coin toss)

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Independence in Real Data

• Check if P(A)P(AB)
• Example LA Dodgers (2000)

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Chapter 7 Probability Distributions
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Random Variable

• The variable of interest is called random
  variable because its value varies depending on
  the result of a particular trial.

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Expected Value and Variance

• Notice that we have different formulas to find
• The mean and variance of the population
• The mean and variance of a sample
• The mean and variance of a sample proportion
• The mean and variance of a random variable
• Many others that we have not covered sample sum,
  sum of random variables, etc.

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Mean and Variance of a Random Variable
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Example
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Example Variance
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Example
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Example
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Example Everyday Situation

• Wisconsin Lottery Big Cat Cash scratch-off
  game.
• Cost 1.00 to play

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Example Everyday Situation

• Wisconsin Lottery Big Cat Cash scratch-off
  game.
• How much should I expect to win?

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Example Everyday Situation

• How much should I expect to win?

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Linear Transformation Rules
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Example

• We want to multiply by 2 and add 5 to the
  largest number from rolling 2 dice.
• What is the mean and variance?
• Create table, find mean, ..
• Or

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Addition and Subtraction Rules
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Addition and Subtraction Rules
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Example
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Example

• What is the mean and variance of the sum of the
  roll of 2 dice?
• Notice the events are independent
• We could draw the table, find the probabilities,
  the expected value.
• Or