lct08 - Introduction to Business Statistics Lecture 8 The...

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1 Introduction to Business Statistics L e c t u r e 8 The Normal Distribution and Other Continuous Distributions Intended learning outcomes Understand the difference between continuous and discrete probability distributions Know how to use uniform probability distributions to model equally likely continuous outcomes Understand the importance of normal random variables and how to find normal probabilities
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2 Introduction For discrete random variables like binomial and hypergeometric ones, the probability distribution assign a positive probability for each value that the random variable can take. Here we consider random variables which can assume infinite many values so much so that we cannot even count them. In this case, the probability that the random variable assumes a particular value can only be zero. How do we describe the probability distribution of such a random variable?
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3 P ( X = x ) 0 1 2 3 4 X 0 1 2 3 4 X f ( x ) x
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4 The probability distribution of a continuous random variable When X is a discrete counting random variable, the graph of P ( X=x ) consists of vertical lines spaced one unit apart. The sum of total heights of all these lines equals one. As we explained, this approach does not work for continuous random variables. What if we use area instead of height to represent probabilities? It works for continuous random variables which can assume infinite many values! We label the vertical axis for a continuous probability distribution as f ( x ) and call it the probability density function of the continuous random variable X. The total area under the curve of f ( x ) must be 1.
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5 Uniform distribution: Density function : f x ba a x b () / ( ) , 1 The mean : E X ab ( ) /
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This note was uploaded on 11/23/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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lct08 - Introduction to Business Statistics Lecture 8 The...

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