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Section 7.1 Discrete and Continuous Random Variables

Section 7.1 Discrete and Continuous Random Variables. AP Statistics. Random Variables. A random variable is a variable whose value is a numerical outcome of a random phenomenon. For example: Flip three coins and let X represent the number of heads. X is a random variable.

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Section 7.1 Discrete and Continuous Random Variables

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  1. Section 7.1Discrete and Continuous Random Variables AP Statistics

  2. Random Variables • A random variable is a variable whose value is a numerical outcome of a random phenomenon. • For example: Flip three coins and let X represent the number of heads. X is a random variable. • We usually use capital letters to denotes random variables. AP Statistics, Section 7.1, Part 1

  3. Random Variables • A random variable is a variable whose value is a numerical outcome of a random phenomenon. • For example: Flip three coins and let X represent the number of heads. X is a random variable. • The sample space S lists the possible values of the random variable X AP Statistics, Section 7.1, Part 1

  4. Discrete Random Variable • A discrete random variable X has a countable number of possible values. • For example: Flip three coins and let X represent the number of heads. X is a discrete random variable. • We can use a table to show the probability distribution of a discrete random variable. AP Statistics, Section 7.1, Part 1

  5. Discrete Probability Distribution Table AP Statistics, Section 7.1, Part 1

  6. Probability Distribution Table: Number of Heads Flipping 4 Coins AP Statistics, Section 7.1, Part 1

  7. Discrete Probability Distributions • Can also be shown using a histogram AP Statistics, Section 7.1, Part 1

  8. AP Statistics, Section 7.1, Part 1

  9. What is the average number of heads? AP Statistics, Section 7.1, Part 1

  10. AP Statistics, Section 7.1, Part 1

  11. Continuous Random Variable • A continuous random variableX takes all values in an interval of numbers. AP Statistics, Section 7.1, Part 1

  12. Distribution of Continuous Random Variable AP Statistics, Section 7.1, Part 1

  13. Distribution of Continuous Random Variable • The probability distribution of X is described by a density curve. • The probability of any event is the area under the density curve and above the values of X that make up that event. AP Statistics, Section 7.1, Part 1

  14. Normal distributions as probability distributions • Suppose X has N(μ,σ) then we can use our tools to calculate probabilities. AP Statistics, Section 7.1, Part 1

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