Statistics

Normal Distribution

A normal distribution is the most common distribution that you will come across in statistics. Before we formally define a normal distribution, let’s first recall two important prerequisites, continuous random variables and probability distribution.


Continuous Random Variable vs Discrete Random Variable

A continuous random variable is a variable whose value ranges from negative infinity to positive infinity. Unlike discrete variables, which have countable values, continuous variables can take on an infinitely small fractional value.

Probability Density Function

A normal distribution is a probability distribution for a continuous random variable that has the following properties:

  1. Mean = Median = Mode
  2. Symmetrical around the Mean
  3. 95% of measurements fall within 2 standard deviations of the mean.

[IMG]

The probability density function of a normal distribution is defined as:

[IMG]

We can measure the probability that variable x is within the range: x_i< x < x_j by calculating the area under the curve from x_i to x_j. A bell curve is used to describe the shape of a normal distribution. For example, the visualizations above, are all bell curves.

Conclusion

In this brief article, we covered the basics of a normal distribution. You now understand the properties of the normal distribution as well as what a bell curve is and how it relates to a normally distributed continuous random variable. In my next tutorial, I will be covering the chi-squared distribution.


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Hypergeometric Distribution