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Chapter7_STAT1100.ppt", filename="Chapter7_STAT1100.ppt", filename="Chapter7_STA

# Chapter7_STAT1100.ppt", filename="Chapter7_STAT1100.ppt", filename="Chapter7_STA

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Random Variables And Discrete Probability Distributions Statistics for Management and Economics Chapter 7

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Objectives Random Variables and Probability Distributions Bivariate Distributions Binomial Distribution Poisson Distribution
Random Variables A random variable is a function or rule that assigns a number to each outcome of an experiment. Alternatively, the value of a random variable is a numerical event. Instead of talking about the coin flipping event as {heads, tails} think of it as “the number of heads when flipping a coin” so we have {1, 0}

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Random Variables Discrete one that takes on a countable number of values Values on the roll of dice: 2, 3, 4, …, 12 Integers Continuous one whose values are not discrete , not countable Values resulting from the event time taken to walk to campus (anywhere from 5 to 30 minutes) Real Numbers
Probability Distributions A probability distribution is a table, formula, or graph that describes the values of a random variable and the probability associated with these values. Since we’re describing a random variable (which can be discrete or continuous) we have two types of probability distributions: Discrete Probability Distribution, (this chapter) Continuous Probability Distribution (Chapter 8)

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Notation An upper-case letter will represent the name of the random variable, usually X . Its lower-case counterpart will represent the value of the random variable. The probability that the random variable X will equal x is: P( X  = x ) …or more simply P( x )
Discrete Probability Distributions The probabilities of the values of a discrete random variable may be derived by means of probability tools such as tree diagrams or by applying one of the definitions of probability, so long as these two conditions apply:

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Discrete Distributions A survey of Amazon.com shoppers reveals the following probability distribution of he number of books purchased per hit: # of books x P( x ) 0 0 0.35 1 1 0.25 2 2 0.20 3 3 0.08 4 4 0.06 5 5 0.03 6 6 0.02 7 7 0.01 e.g. P( X =4) = P(4) = 0.06 = 6% What is the probability that a shopper buys at least one book, but no more than 3 books? P(1 ≤ X ≤ 3) = P(1) + P(2) + P(3) = 0.25 + 0.20 + 0.08 = 0.53
Developing a Probability Distribution Probability calculation techniques can be used to develop probability distributions, for example, a new game in Vegas is developed where a fair coin is tossed three times. What is the probability distribution of the number of heads if I play this game in Vegas? Let H denote success, i.e. flipping a head P(H)=.50 Thus H C is not flipping a head, and P(H C )=.50

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Probability Distribution The discrete probability distribution represents a population Since we have populations , we can describe them by computing various parameters .
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