Bluman, Chapter 5
In how many ways can the letters in the following words be arranged? Fancy Algebra Mississippi Hannah Bluman, Chapter 5
A family has four children. Let x be the number of boys in the family find: 𝑃(0) 𝑃(1) 𝑃(2) 𝑃(3) 𝑃(4) Bluman, Chapter 5
October calendar is posted online Bluman, Chapter 5
Discrete Probability Distributions Chapter 5 Discrete Probability Distributions McGraw-Hill, Bluman, 7th ed, Chapter 5
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
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
Variables Discrete variables have a finite number of possible values or an infinite number of values that can be counted. Result of a count. Continuous variables are variables that can assume all values in the interval between any two given values. Result of a measurement.
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
Chapter 5 Discrete Probability Distributions Section 5-1 Example 5-1 Page #254 Bluman, Chapter 5
Example 5-1: Rolling a Die Construct a probability distribution for rolling a single die. Bluman, Chapter 5
Chapter 5 Discrete Probability Distributions Section 5-1 Example 5-2 Page #254 Bluman, Chapter 5
Example 5-2: Tossing Coins Display the probability distribution for tossing three coins. If x is the number of heads. . Bluman, Chapter 5
Example 5-2: Tossing Coins Represent graphically the probability distribution for the sample space for tossing three coins. . Bluman, Chapter 5
Requirements for Prob Dist. 𝑝 𝑥 =1 0≤𝑝(𝑥)≤1 Bluman, Chapter 5
Example 5-3 During the summer months, a rental agency keeps track of the number of chain saws it rents each day during a period of 90 days. The number of saws rented per day is represented by the variable x. The results are shown here. Compute the probability P(x) for each x, and construct a probability distribution and graph for the data. x Number of Days 0 45 1 30 2 15 Total 90
On your Own Read Example 5-4 page 257 Applying Concepts page 257 Exercises 5-1 page 258 # 1-18 all, 23 and 27. Bluman, Chapter 5