Math 1025 - Lesson Plan Chapter 4

Math 1025 - Lesson Plan Chapter 4 - Chapter 4 - Discrete...

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Chapter 4 - Discrete Probability Distributions Section 4.1 - Probability Distributions Objectives Distinguish between discrete random variables and continuous random variables Construct a discrete probability distribution and its graph Determine if a distribution is a probability distribution Find the mean, variance, and standard deviation of a discrete probability distribution Find the expected value of a discrete probability distribution 1) Random Variable (x) - Represents a numerical value associated with each outcome of a probability distribution. Denoted by x. 2) Discrete Random Variable - Has a finite or countable number of possible outcomes that can be listed. 3) Continuous Random Variable - Has an uncountable number of possible outcomes, represented by an interval on the number line. Example 1 & Try It Yourself 1 (p. 195) - Decide whether the random variable x is discrete or continuous. Explain. (1) x represents the number of stocks in the Dow Jones Industrial Average that have price increases in a given day. (2) x represents the volume of water in a 32-oz. container. TIY #1 (1) x represents the length of time it takes to complete a test. (2) x represents the number of songs played by a band at a rock festival. a. Decide if x represents counted data or measured data. b. Make a conclusion and explain your reasoning. 4) Discrete probability distribution - Lists each possible value the random variable can assume, together with its probability. Must satisfy the following conditions: (i) The probability of each value of the discrete random variable is between 0 and 1, inclusive {0 P ( x ) 1}. (ii) The sum of all the probabilities is 1 (iii) To Construct a Discrete Probability Distribution: Make a frequency distribution for all the outcomes and find the relative frequencies. {all possible x's are the outcomes and the relative frequencies are the probabilities of each outcome}. Try It Yourself 2 -Modified (p. 196) - A company tracks the number of sales new employees make each day during a 100-day probationary period. The results for one new E'ee are shown in the table. Construct and graph a probability distribution. a. Find the Probability of each outcome. b. Organize the probabilities in a probability distribution. c. Graph the probability distribution using a histogram. Sales per day, x Number of days, f 0 16 1 19 2 15 3 21 4 17 5 12 Total 100 Try It Yourself 3 - (p. 197) - Verify that the distribution in TIY #2 is a probability distribution.

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This note was uploaded on 02/07/2012 for the course MATH 1025 taught by Professor Raney during the Fall '10 term at Metro State.

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Math 1025 - Lesson Plan Chapter 4 - Chapter 4 - Discrete...

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