![]() Figure 2: example of gaussian distribution for different values of the standart deviation (\(\sigma\)) and different values of the mean (\(\mu\)). The area under the curve is 1 no matter which standard deviation you chose. Note in the figure below that when the standard deviation is smaller the curve is higher. $$p(x) = \mathcal(0,1)\) is called the standard normal distribution (figure 1).Īdvanced: add in a future revision of the lesson to show that the expected value of the standard normal distribution is 0, the area under the curve is 1 and the standard deviation is 1\. The equation for this distribution is a bit complex: The gaussian or normal distribution has a typical bell-shaped curve (see figure 1). You can use Grapher on Mac and Gnuplot on Linux. If you reproduce these curves for yourself, you will probably get a better sense of what the parameters of the equation do. We will see it appearing in the next chapter as well. ![]() For example, the adult height in any adult given population generally follows (more or less) a normal distribution. Why study the normal distribution? This distribution is very common in nature. We now have the knowledge needed to introduce and understand its equation. In chapter 2, we have mentioned the normal (or gaussian) probability distribution. Probability Distribution: Part 2 Reading time: 3 mins. Expected Value of the Function of a Random Variable: Law of the Unconscious Statistician.Probability Density Function (PDF) and Cumulative Distribution Function (CDF). ![]()
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