5. Suppose that X1, X2, ..., X are i.i.d N(0,1), where 0 E R is unknown....

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5. Suppose that X1, X2, ..., X are i.i.d N(0,1), where 0 E R is unknown. Let p = Po(X1 > 0). (a) Find the maximum likelihood estimator b of t. (b) Find an approximate 95% confidence interval for . 1,...,n. Define = (1/n) Yi. Show that b is a (c) Let Y; = 1{X; > 0}, for i consistent estimator of p. (d) Which estimator of , or b, is more preferable in this model. 5. Suppose that X1, X2, ..., X are i.i.d N(0,1), where 0 E R is unknown. Let p = Po(X1 > 0). (a) Find the maximum likelihood estimator b of t. (b) Find an approximate 95% confidence interval for . 1,...,n. Define = (1/n) Yi. Show that b is a (c) Let Y; = 1{X; > 0}, for i consistent estimator of p. (d) Which estimator of , or b, is more preferable in this model.