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Lecture13_print - MA/STAT416 Probability Lecture Notes...

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MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 9: The Normal Distribution April 21, 2011 9 The Bell Shape Distribution 9.1 History The normal distribution is the most common, popular model for continuous random variables. Data collected on many types of random variables in daily life approximately follow normal distribution. This empirical phenomenon can be partially explained by means of mathematical theorems. But some of it is still a mystery. Another reason for historical importance of the normal distribution is that many methods that statisticians use are based on the assumption that the random variable in consideration has a normal distribution. Normal distributions are characterized by two parameters, the mean μ , and variance σ 2 . If we know these two quantities, then any probability can be calculated for normal distributions. If X is a random variable, we say X N ( μ, σ ). If μ = 0 and σ = 1, then the distribution is called standard normal. A random variable having
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