Probability Distributions: Gaussian Distribution

Gaussian or normal distribution

The Gaussian, or normal distribution, is a continuous probability distribution used for experiments with real-valued outputs. It is widely used in statistics and data science and is commonly observed in many real-world values, which is why it is also known as the normal distribution.

Some examples of normal distribution in the world are:

• The height of people on a football team.
• The blood pressure of young people in a family.
• The results of an annual test at a university.

The normal distribution is represented graphically, as seen below. It is also referred to as a Bell Curve. On the y-axis, we have the probability of a certain outcome, and on the x-axis, we have the outcomes.

Properties of normal distribution

Normal distribution has the following characteristics:

• In a normal distribution, the mean, median, and mode are all equal.

• Normal distribution is symmetric about the center (mean).

• It has 50% of the values above the mean and 50% of the values below the mean. It is also obvious from the graphical representation above.

• The total area under the curve shown above is 1.

Probability density function

The probability density function for a normal distribution is displayed below:

$g(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{\frac{-1}{2\sigma^2}(x-\mu)^{2}}, -\infty < x < \infty$ ...