TRUE OR FALSE The standard deviation of the chisquare distri

TRUE OR FALSE? The standard deviation of the chi-square distribution is twice the mean. Why?

Solution

False. the variance of a chi-square distribution is twice the mean. not the standard deviation.

let X~chi-square distribution with degrees of freedom=n

then mean=E[X]=n

variance=V[X]=2n

so standard deviation=sqrt(2n) which is not equal to 2n=2*n=2*E[X]

so the statement is FALSE.