Chi-square Density Function The probability density curve of a Chi-square distribution is an asymmetric curve stretching over the positive side of the line and having a long right tail. The form of the curve depends on the value of a parameter known as the degree of freedom (d.f.). The expected value of Chi-square statistic is its d.f., its variance is twice of its d.f., and its mode is equal to (d.f.- 2). Chi square Distribution relation to Normal Distribution: The Chi-square distribution is related to the sampling distribution of the variance when the sample is from a normal distribution. The sample variance is a sum of squares of standard normal variables N (0, 1). Hence, the of square of N (0,1) random variable is a Chi-square with 1 d.f. . Notice that the Chi-square is related to F-statistics as follows: F = Chi-square/d.f. 1 , where F has (d.f. 1 = d.f. of the Chi-square-table, and d.f. 2
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