From the course: Probability Foundations for Data Science

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Chi-squared distribution

Chi-squared distribution

From the course: Probability Foundations for Data Science

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Chi-squared distribution

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- [Instructor] Up next is the chi-squared distribution. The chi-squared distribution works with continuous random variables, where it models the sum of squares of a defined amount of independent standard normal variables. This distribution is heavily used in hypothesis testing and for creating confidence intervals. The chi-squared distribution is defined by one variable. This variable is k, and it represents the degrees of freedom. This is what represents the number of independent standard normal variables being summed. If Z1 to Zk are independent standard normal variables, then the sum of these can be represented by the following equation. So you're finding your random variable X, and this is equal to the sum of i equal to one to your value k of Zi squared. This is often denoted in one of two ways where you have x being approximately chi squared, where it's denoted in parentheses with a k, or sometimes the k is a subletter for the chi-squared portion. The chi-squared distribution is…

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