Chi | variance chi square distribution
byMarcoTaboga[1],PhD ArandomvariablehasaChi-squaredistributionifitcanbewrittenasasum ofsquaresofindependentstandardnormalvariables. Sumsofthiskindareencounteredveryofteninstatistics,especiallyinthe estimationof variance[2]andinhypothesistesting. Inthislecture,wederivetheformulaeforthemean,thevarianceandother characteristicsofthechi-squaredistribution. Degreesoffreedom Wewillprovebelowthatarandomvariable hasaChi-squaredistributionifitcanb...
A random variable has a Chi-square distribution if it can be written as a sum of squares of independent standard normal variables.
Sums of this kind are encountered very often in statistics, especially in the estimation of variance[2] and in hypothesis testing.
In this lecture, we derive the formulae for the mean, the variance and other characteristics of the chi-square distribution.
Degrees of freedomWe will prove below that a random variable has a Chi-square distribution if it can be written aswhere , ..., are mutually independent standard normal random variables[3].
The number of variables is the only parameter of the distribution, called the degrees of freedom parameter. It determines both the mea...