Question

The relationship between the mean and the variance of x square with n degrees

of freedom is:
mean = Vvariance
mean = variance
mean = 2variance
2mean = variance
none of the above​

Answer 1

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.

Answer 2

Answer:

The correct relationship is mean = n * variance.

Step-by-step explanation:

The relationship between the mean and the variance of x square with n degrees of freedom is:

mean = n * variance

This means that the mean of the distribution of x square is equal to the product of the degrees of freedom (n) and the variance of the distribution.

Therefore, none of the options given in the question is correct. The correct relationship is mean = n * variance.

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