Let Xi be a random variable distributed normal with mean = i and variance = i^2.
Assume that the random variables X1, X2 and X3 are independent.
Using these properties of X1, X2, X3:
a.) give a statistic formula that has a chi-square distribution with 3 degrees of freedom. - Explain.
b.) give a statistic formula that has an F distribution with 1 and 2 degrees of freedom. - Explain.
c.) give a statistic formula that has a t distribution with 2 degrees of freedom. - Explain.
For part a, I did:
[(n - 1)*s²]/σ² ~ X^2 and (n-1) degrees of freedom
So, [3 * s²]/σ² would be ~ X^2 with 3 degrees of freedom if I am doing this correctly
For part b:
I know that the F distribution is defined as: F = (u/v1)/(w/v2) where u = chi-square with v1 degrees of freedom and w = chi-square with v2 degrees of freedom.
I'm not really sure about how to apply it to the problem, though