chapter6 - 2011/09/13 Introduction to Probability and...

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2011/09/13 1 Introduction to Probability and Statistics Thirteenth Edition Chapter 6 The Normal Probability Distribution Continuous Random Variables • Continuous random variables can assume the infinitely many values corresponding to points on a line interval. Examples: –Heights, weights –length of life of a particular product – experimental laboratory error Continuous Random Variables • A smooth curve describes the probability distribution of a continuous random variable. •The depth or density of the probability, which varies with x , may be described by a mathematical formula f ( x ) , called the probability distribution or probability density function for the random variable x . Properties of Continuous Probability Distributions • The area under the curve is equal to 1. • P(a x b) = area under the curve between a and b. •There is no probability attached to any single value of x . That is, P( x = a) = 0. Continuous Probability Distributions There are many different types of continuous random variables We try to pick a model that Fits the data well Allows us to make the best possible inferences using the data. One important continuous random variable is the normal random variable . The Normal Distribution deviation. standard and mean population the are and 1416 . 3 7183 . 2 for 2 1 ) ( 2 2 1   e x e x f x • The shape and location of the normal curve changes as the mean and standard deviation change.
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chapter6 - 2011/09/13 Introduction to Probability and...

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