Question: Distribution statistics problem, please see screenshot. Thank you for your time and help. (a) Suppose X1, X2, .., Xn are independently drawn from N(2, 4).

Distribution statistics problem, please see screenshot. Thank you for your time and help.

(a) Suppose X1, X2, .., Xn are independently drawn from N(2, 4). (i) What is the distribution of !(X1 + X2)? (Give the mean and variance as well. ) (ii) What is the distribution of !(X, + X2+ ... + X.)? (Give the mean and variance as well). As n - co, what do the mean and variance converge to? (iii) What is the distribution of (X1+ X2+ ...+ X.)? (Give the mean and variance as well). As n - co, what do the mean and variance converge to

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