Probability theory: Chi-Squared distribution

This is part of the course “Probability Theory and Statistics for Programmers”.

Probability Theory For Programmers

The Chi-Squared distribution is a continuous probability distribution that is widely used in statistical inference. And it related to the standard normal distribution. If a random variable X has the standard normal distribution, then has the the Chi-Squared distribution with one degree of freedom.

A relation between standard normal distribution and Chi-Squared distribution goes father than this. If we have n independent standard normal random variables, then their sum has a Chi-Squared distribution with n degrees of freedom.

Now let’s plot Chi-Squared distribution with different degrees of freedom.

The mean and variance of Chi-Squared distribution:

mean and variance

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