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Warm-up

Understand the difference between discrete and continuous variables, and learn how to construct a probability distribution for a random variable. Find the mean, variance, standard deviation, and expected value for a discrete random variable, and calculate probabilities for outcomes using different types of distributions.

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Warm-up

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  1. Warm-up Explain the difference between a discrete and a continuous variable. Write a probability distribution for the outcomes of the sum of two dice.

  2. Chapter 5 Overview Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation, and Expectation 5-3 The Binomial Distribution 5-4 Other Types of Distributions Bluman, Chapter 5 2

  3. Chapter 5 Objectives Construct a probability distribution for a random variable. Find the mean, variance, standard deviation, and expected value for a discrete random variable. Find the exact probability for X successes in n trials of a binomial experiment. Find the mean, variance, and standard deviation for the variable of a binomial distribution. Find probabilities for outcomes of variables, using the Poisson, hypergeometric, and multinomial distributions. Bluman, Chapter 5 3

  4. 5.1 Probability Distributions A random variable is a variable whose values are determined by chance. A discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. The sum of the probabilities of all events in a sample space add up to 1. Each probability is between 0 and 1, inclusively. Bluman, Chapter 5 4

  5. Example 5-1: Rolling a Die Construct a probability distribution for rolling a single die. Bluman, Chapter 5 5

  6. Example 5-2: Tossing Coins Represent graphically the probability distribution for the sample space for tossing three coins. . Bluman, Chapter 5 6

  7. Baseball World Series Find P(X) for each X, construct a probability distribution, and draw a graph for the data. Bluman, Chapter 5 7

  8. Two requirements for a probability distribution: • The sum of the probabilities of all events in the sample space must equal 1, that is • The probability of each event in the sample space must be between or equal to 0 or 1. That is, 0 < P(X) < 1.

  9. Applying the Concepts 5-1(bottom of pg 257 and top of pg 158) Bluman, Chapter 5 10

  10. Classwork and Assignment • CW: pg 258: 1-6, 19, 30 • Assignment: pg 258: 7-11 odd, 12-18 all, 20-26 even, 27, 29

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