Chi squared test for goodness of fit
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Cumulative distribution function.
For a discrete random variable cumulative frequencies and probabilities are found by adding together frequencies or probabilities up to a given value. For instance, given the discrete probability distribution. [Table goes here &- download the original to see it.] [Table.] For a continuous probability distribution with probability density function f(x) the probabilities are given by areas under the curve f(x). Thus, the cumulative probability distribution is to a given value xi the area under curve f(x) from [Equation goes here &- download the original to see it.] to xi. [Diagram.] Hence if X is a random variable with probability density function f(x), then the cumulative distribution function of X is given by [Equation.] We proceed to illustrate this result&: Example A continuous random variable X has probability density function [Equation.] Find the cumulative distribution function for X. [Equation.] [Equation.]
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Contents of
Chi squared test for goodness of fit
1 Medians, quartiles and percentiles.
2 Modelling of theoretical distributions to given data and the Chi squared test for goodness of fit
3 Approximation by the chi squared test
4 Example of modelling using the chi squared test for goodness of fit
5 Cumulative distribution function.
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