Problem 31 Let X1, X2, X3, ... be independent N (1,02) random variables. It is known that p > 10. μ (i) (3 pts.) Determi

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Problem 31 Let X1, X2, X3, ... be independent N (1,02) random variables. It is known that p > 10. μ (i) (3 pts.) Determine, in terms of u and o, the constant a such that for all e > 0, x} + → 0 P [ *? + X3 ->] 12 as n → (ii) (4 pts.) Let rn(x) be the relative frequency of the event {X; > x} in the sample (X1,...,xn). Express, in terms of p, o and the unit Gaussian cdf (-), the constant b(r) such that P[rn(2) - 6(2) > ] + 0 as no. a (iii) (8 pts.) Suppose that for a large value of n, it is found that x} + ... + x2 = 296.0 and rn (24.2) = 6.68% n What are your estimates (î, ô) of (u, o)? (Use NORMINV in MATLAB, then solve a quadratic.) (iv) (5 pts.) What is the approximate value of rn (26.8) in the sample of part (iii)?