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In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables.
May 20, 2022 · Learn what chi-square distributions are, how they are related to the standard normal distribution, and how they are used in hypothesis tests. See graphs, formulas, properties, and examples of chi-square distributions with different degrees of freedom.
- As the degrees of freedom ( k ) increases, the chi-square distribution goes from a downward curve to a hump shape. As the degrees of freedom incr...
- A chi-square distribution is a continuous probability distribution . The shape of a chi-square distribution depends on its degrees of freedom ,...
- The two main chi-square tests are the chi-square goodness of fit test and the chi-square test of independence .
Learn how to define, derive and apply the Chi-square distribution, a probability distribution of a sum of squares of independent standard normal variables. See density plots, proofs, examples and exercises with solutions.
Apr 2, 2023 · The chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whether the distributions of two populations are the same, (iii) whether two events might be independent, and (iv) whether there is a different ...
Chi-Square Distribution. The distribution of the chi-square statistic is called the chi-square distribution. In this lesson, we learn to compute the chi-square statistic and find the probability associated with the statistic. And we'll work through some chi-square examples to illustrate key points.
In this video, we'll just talk a little bit about what the chi-square distribution is, sometimes called the chi-squared distribution. And then in the next few videos, we'll actually use it to really test how well theoretical distributions explain observed ones, or how good a fit observed results are for theoretical distributions.
- 10 min
- Sal Khan
Learn how chi-square distributions are derived from gamma distributions and how they depend on the degrees of freedom. Find the moment generating function, mean and variance of chi-square distributions and see examples.
