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Review

Review. 3.3 Percentiles and Box-and-Whisker Plots Chapter 4 Elementary Probability Theory Chapter 5 The Binomial Probability Distribution and Related Topics. 3.3 Percentiles and Box-and-Whisker Plots. Percentiles Quartiles Box-and-Whisker Plots. Probability Assignment.

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Review

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  1. Review • 3.3 Percentiles and Box-and-Whisker Plots • Chapter 4 Elementary Probability Theory • Chapter 5 The Binomial Probability Distribution and Related Topics

  2. 3.3 Percentiles and Box-and-Whisker Plots • Percentiles • Quartiles • Box-and-Whisker Plots

  3. Probability Assignment Assignment by intuition – based on intuition, experience, or judgment. Assignment by relative frequency – P(A) = Relative Frequency = Assignment for equally likely outcomes

  4. The Sum Rule and The Complement Rule The sum of the probabilities of all the simple events in the sample space must equal 1. The complement of event A is the event that Adoes not occur, denoted by Ac P(Ac) = 1 – P(A)

  5. Multiplication Rule for Independent Events General Multiplication Rule – For all events (independent or not): Conditional Probability (when ):

  6. Mutually Exclusive Events Two events are mutually exclusive if they cannot occur at the same time. Mutually Exclusive = Disjoint If A and B are mutually exclusive, then P(A and B) = 0

  7. Addition Rules If A and B are mutually exclusive, then P(A or B) = P(A) + P(B). If A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B).

  8. Multiplication Rule for Counting This rule extends to outcomes involving three, four, or more series of events.

  9. Factorials For counting numbers 1, 2, 3, … ! is read “factorial” So for example, 5! is read “five factorial” n! = n * (n-1) * (n-2) * … * 3 * 2 * 1 So for example, 5! = 5 * 4 * 3 * 2 * 1 = 120 1! = 1 0! = 1

  10. Permutations Permutation: ordered grouping of objects. Counting Rule for Permutations

  11. Combinations A combination is a grouping that pays no attention to order. Counting Rule for Combinations

  12. Chapter 5 The Binomial Probability Distribution and Related Topics • Introduction to Random Variables and Probability Distribution • Binomial Probabilities • Additional Properties of the Binomial Distribution • The Geometric and Poisson Probability Distributions

  13. 5.1 Introduction to Random Variables and Probability Distribution Statistical Experiments – any process by which measurements are obtained. A quantitative variable, x, is a random variable if its value is determined by the outcome of a random experiment. Random variables can be discrete or continuous.

  14. Random Variables and Their Probability Distributions Discrete random variables – can take on only a countable or finite number of values. Continuous random variables – can take on countless values in an interval on the real line Probability distributions of random variables – An assignment of probabilities to the specific values or a range of values for a random variable.

  15. Means and Standard Deviations for Discrete Probability Distributions

  16. Finding µ and σ forLinear Functions of x

  17. Combining Random Variables

  18. 5.2 Binomial Experiments There are a fixed number of trials. This is denoted by n. The n trials are independent and repeated under identical conditions. Each trial has two outcomes: S = success F = failure

  19. Binomial Experiments For each trial, the probability of success, p, remains the same. Thus, the probability of failure is 1 – p = q. The central problem is to determine the probability of r successes out of n trials.

  20. Binomial Probability Formula

  21. Determining Binomial Probabilities Use the Binomial Probability Formula. Use Table 3 of Appendix II. Use technology.

  22. 5.3 Graphing a Binomial Distribution

  23. Mean and Standard Deviation of a Binomial Distribution

  24. 5.4 The Geometric Distribution Suppose that rather than repeat a fixed number of trials, we repeat the experiment until the first success. Examples: Flip a coin until we observe the first head Roll a die until we observe the first 5 Randomly select DVDs off a production line until we find the first defective disk

  25. The Poisson Distribution

  26. Poisson Approximation to the Binomial

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