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.