Question

Decide whether the following statements are true or false;

The standard deviation of the chi-square distribution is twice the mean.

Short answer

The statement is false.

Step-by-step solution

Given Infromation

The standard deviation of the chi-square distribution is twice the mean.

Explanation

To check whether the given statement is true or false:

The standard deviation of the chi-square distribution is twice the mean.

The mean of ${\chi }^2$distribution with $n$degrees of freedom is $n$.

Variance of ${\chi }^2$distribution with $n$degrees of freedom is $2n$. This means that standard deviation is $\sqrt{2n}$.

Therefore, the statement is false.