MA/STAT416: ProbabilityLecture NotesSpring 20111Chapter 9: The Normal DistributionApril 21, 20119The Bell Shape Distribution9.1HistoryThe normal distribution is the most common, popular model for continuous randomvariables. Data collected on many types of random variables in daily life approximatelyfollow normal distribution. This empirical phenomenon can be partially explained bymeans of mathematical theorems. But some of it is still a mystery. Another reason forhistorical importance of the normal distribution is that many methods that statisticiansuse are based on the assumption that the random variable in consideration has a normaldistribution. Normal distributions are characterized by two parameters, the meanμ, andvarianceσ2.If we know these two quantities, then any probability can be calculatedfor normal distributions. IfXis a random variable, we sayX∼N(μ, σ).Ifμ= 0andσ= 1, then the distribution is called standard normal. A random variable having
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