Question

The relationship between mean and variance of X square with n degree of freedom

Answer 1

Suppose we select a random sample of size $n$ from a normal population, having a standard deviation equal to σ. We find that the standard deviation in our sample is equal to s. Given these data, we can define a statistic, called chi-square. 

The mean of the distribution is equal to the number of degrees of freedom.

The variance of the distribution is equal to two times the number of degrees of freedom.

2mean = variance