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Understanding Factorials and Binomial Probability Functions: A Comprehensive Guide

This guide provides an in-depth exploration of factorial functions and the combinations rule, illustrated with examples. It delves into binomial probability experiments, the notation used in distributions, and how to construct and compute binomial distributions, including cumulative probabilities. You'll also learn about the mean and variance of a binomial random variable, and the interpretation of standard deviations. Practical examples demonstrate these concepts, making it easier to understand and apply binomial distributions effectively.

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Understanding Factorials and Binomial Probability Functions: A Comprehensive Guide

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Presentation Transcript

    2. The Factorial Function

    3. Example 1: Computing Factorials

    4. Combinations Rule

    5. The Combinations Rule

    6. Example 2: Computing with the Combinations Rule

    7. Criteria for a Binomial Probability Experiment

    8. Notation Used in the Binomial Probability Distribution

    9. Illustration: Constructing a Binomial Distribution

    12. The Binomial Probability Distribution Function

    13. Binomial Distribution Function on the TI-83

    14. Example 3: Computing Binomial Probabilities

    15. Cumulative Binomial Probabilities

    17. Example 4: Computing Cumulative Binomial Probabilities

    18. Example 5: Using the Binomial Probability Distribution Function

    21. The Mean and Variance of a Binomial Random Variable

    22. Example 6: Finding the Mean and Standard Deviation

    23. Binomial Probability Distributions

    25. Bell-Shaped Binomial Distributions

    26. Interpreting Standard Deviation

    27. Example 7: Applying the Empirical Rule

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