Physics307L F08:Schedule/Week 5 agenda/Normal

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 μ and standard deviation σ is

$f(x) = \frac{1}{\sigma\sqrt{2\pi}} \, e^{ -\frac 12 \left( \frac{x- \mu}{\sigma}\right)^2 }$.

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