CSCI 3022 Lecture Notes - Lecture 12: Probability Distribution, Standard Normal Deviate, Normal Distribution
6 Mar 2019
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Document Summary
The normal distribution (aka, gaussian distribution) is probably the most important and widely used distribution in probability and statistics. Many populations have distributions well-approximated by a normal distribution. It"s very important to check that normal is a good approximation through! A continuous random variable x has a normal (or gaussian) distribution with parameters and if its probability density function is given by. We say x~n( , ) the standard normal distribution: the normal distribution with parameter values =0, =1. A standard normal variable is usually denoted z. Recall: the normal distribution does not have a closed form cumulative distribution function (cid:736) we use special notation to denote the pdf of the standard normal distribution: (z) = p(z (cid:15457) z) (cid:736) and usually we just look up values for (z) in a table. The standard normal distribution rarely occurs in real life. Instead, we take non- standard normal distributions, and standardize them using a simple transformation.
