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Wednesday, January 16, 2008

Write down the properties of Chi-square distribution

Ans. Properties of χ2 distribution:

1. Mean of χ2 distribution = Degrees of freedom = V

2. SD of χ2 distribution = √2V

3. Median of χ2 distribution divides the area of the curve into two equal parts, each part being 0.5

4. Mode of χ2 distribution is equal to degrees of freedom less 2 i.e., V-2

5. χ2 values are always positively skewed.

6. χ2 values increase with the increase in the DF, there is a new χ2 distribution with every increase in the no. of degrees of freedom.

7. The lowest value of χ2 is zero and the highest is infinity i.e. 0 < χ2 <

8. When two chi-squares γ 2\1 and χ2/2 are independent following χ2 distribution with n1 and n2 degrees of freedom, their sum χ2/2 +χ2/2 will follow χ2 distribution with n1 + n2 degrees of freedom.

9. When V>30, √2χ2 - √2V -1 approximately follows the standard normal distribution.

Chi-Square Distribution:

This article is about the mathematics of the chi-square distribution. For its uses in statistics, see Chi-Square Test.

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