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Let Xi be a random variable distributed normal mean i & 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.

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