1 thought on “The relationship between the mean and the variance of x square with n degrees<br /><br />of freedom is:<br />mean = Vvariance<br /”
If X is normally distrubuted with zero mean and unit variance, then what is the mean and variance of X^2 equal to?
X ~ N(0, 1)
⟹X2 ~ χ2(1)
⟹μX2=1 and σ2X2=2μ=2.
In words, this says that if X is a standard normal random variable, then X2 is distributed chi-square with one degree of freedom. The mean of X2 is the number of degrees of freedom and its variance is twice the number of degrees of freedom.
If X is normally distrubuted with zero mean and unit variance, then what is the mean and variance of X^2 equal to?
X ~ N(0, 1)
⟹X2 ~ χ2(1)
⟹μX2=1 and σ2X2=2μ=2.
In words, this says that if X is a standard normal random variable, then X2 is distributed chi-square with one degree of freedom. The mean of X2 is the number of degrees of freedom and its variance is twice the number of degrees of freedom.
Your answer will be none of the above.