Lct05 - Introduction to Business Statistics Lecture 5...

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1 Introduction to Business Statistics Lecture 5 Random Variables and Discrete Probability Distributions In the probability theory we developed so far, there is one obvious weakness. The way we define and describe events renders problem solving ineffective sometimes. The situation is very much like arithmetic versus algebra. Random Variables: In an experiment, if we associate each possible outcome with a number and designate a variable X to represent the outcome of the experiment, then we have a random variable. In short, a random variable is a variable taking different values according to chance. The uncertainty in a random variable is described by its probability distribution.
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2 The Probability Distribution ( of a random variable ) can be viewed as the frequency distribution of a population. The frequency distribution of a data set is an empirical object that describes what has been observed. Here the frequency distribution of a population is a theoretical object that serves as a model for thinking and understanding. Consider the frequency distribution of 296 workers’ test scores and the probability distribution of the following random variable Event Random Variable X Probability P ( X = x ) 5 E 5 X 0.34% 8 E 8 X 0.34% 24 E 24 X 8.45% 25 E 25 X 4.05%
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3 Example1: ( Demand for product with short useful life ) A wholesaler sells strawberries. If not sold on the day of delivery, it is worthless. To find out how many cases of strawberries to order before the beginning of each business day, he studied the daily demand. The record of the last one hundred business days yields the following. Daily Demand (cases) # of Days Relative Frequency 10 15 0.15 11 20 0.20 12 40 0.40 13 25 0.25 Suppose that you view the daily demand as a random variable X with a probability distribution same as the frequency distribution. What is the probability that the daily demand is higher than 11? lower than 12? Is it
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Lct05 - Introduction to Business Statistics Lecture 5...

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