Introduction to Probability Function (Part2)

2. Normal Distribution

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

The normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as Cauchy’s, Student’s, and logistic). The terms Gaussian function and Gaussian bell curve are also ambiguous because they sometimes refer to multiples of the normal distribution that cannot be directly interpreted in terms of probabilities.

The probability density of the normal distribution is:

 f(x \; | \; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi} } \; e^{ -\frac{(x-\mu)^2}{2\sigma^2} }
Here, \mu is the mean or expectation of the distribution (and also its median and mode). The parameter \sigma is its standard deviation with its variance then \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
Image result for normal distribution

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