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:
- Mean = Median = Mode
- Symmetrical around the Mean
- 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.