Physics307L F07:Schedule/Week 5 agenda/Normal

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Normal Distribution

The normal or Gaussian distribution is a thing of beauty, appearing in many places in nature. This probably is a result of the normal distribution resulting from the law of large numbers, by which a sum of many random variables (with finite variance) becomes a normally distributed random variable according to the central limit theorem.

Also known as the bell curve, the normal distribution has been applied to many social situations, but it should be noted that its applicability is generally related to how well or how poorly the situation satisfies the property mentioned above, whereby many finitely varying, random inputs result in a normal output.

The formula for the density f of a normal distribution with mean Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \mu} and standard deviation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \sigma} is

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle f(x) = \frac{1}{\sigma\sqrt{2\pi}} \, e^{ -\frac 12 \left( \frac{x- \mu}{\sigma}\right)^2 }} .

A rather thorough article in Wikipedia could be summarized to extend the usefulness of this book: Normal distribution from Wikipedia.