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7.1 Probability Distributions

7.1 Probability Distributions. Random Variables. A Random Variable, X, has a single value for each outcome in an experiment. Example, if X is the number rolled with a die, then x has a different value for each of the six possible outcomes. Continuous Vs. Discrete.

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7.1 Probability Distributions

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  1. 7.1 Probability Distributions

  2. Random Variables • A Random Variable, X, has a single value for each outcome in an experiment. • Example, if X is the number rolled with a die, then x has a different value for each of the six possible outcomes.

  3. Continuous Vs. Discrete • Discrete Variables have values that are separate from each other and the number of possible values can be small. • Continuous Variables have an infinite number of possible values in a continuous interval

  4. Random Variables • The number of phone calls made by a sales person • The length of time the salesperson spent on the telephone • A company’s annual sales • The number of widgets sold by the company • The distance from earth to the sun

  5. Uniform Probability

  6. Probability Distributions • In certain situations the number of times something happens usually follows a pattern. These patterns are analyzed and grouped into distributions.

  7. Probability Distribution • grades in a class, follow a normal distribution. • Binomial Distribution, Bernoulli, Chi Squared, Poisson, etc.

  8. Uniform Discrete Distribution • When the probabilities for each outcome is the same, it is grouped in the Uniform Probability Distribution

  9. Rolling 1 Die • P(X=1) • P(X=2) • P(X=3) • P(X=4) • P(X=5) • P(X=6)

  10. Uniform Discrete Distribution

  11. Expected Value • Sometimes it is helpful to be able to predict the average value that will occur within a situation.

  12. Expected Value

  13. Dice Game • Consider a simple game in which you roll a single die. If you roll an even number, you gain that number of points and if you roll an odd number you lose that number of points. • Show the probability Distribution of points in this game. • What is the expected number of points per roll? • Is this game fair? Why?

  14. Canoes • A summer camp has seven 4.6-m canoes, ten 5.0-m canoes, four 5.2m canoes, and four 6.1-m canoes. Canoes are assigned randomly for campers going on a canoe trip. • Show the probability Distribution for the length of an assigned canoe. • What is the expected length of the canoe?

  15. Assignment • pg 376 #’s 1-6,12

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