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Hi plz help me with statistic question below and write down detailed steps for each part, thank you!

8. Suppose that we wish to evaluate I(f)f(x)dx Let g be a density function on [x1, 2]. Generate X. .. .X, from g and estimate / by 1 f(X) 1(f) = n 2 g(X) (i) Show that E [I(f)]-1(f). (i) Find an expression for the Varli()l. Give an example for which it is finite and an example for which it is infinite. Note that if it is finite, the law of large number implies that Of)-1(f) and (ii) If x0,2 and g is uniform, use this to evaluate the integral in question iv) Can the estimate in question 1 be improved by choosing g to be other than uniform distribution? Hint: compare variances)

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8)

》 f(x) Νο ο Σ Cf (f)]. (수(f)s@AX 90x) d40 I0)

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