Exercises for Tue Sep 1: ¡­

Exercises for Tue Sep 1:

Extra 3: We have shown "the continuity lemma", that Xn to a in probability implies g(Xn) to g(a) in probability, if only g is continuous at the point x = a [cf. Theorem 2.1.4]. Now demonstrate the extended version, where the limit is a random variable X rather than merely a constant a: Xn to X in probability implies g(Xn) to g(X) in probability, if g is continuous (in the region that X falls).

Then, from ELL's exercises for Ch 2: rest of 1.8, then 1.7, 1.9, 2.1, 2.9, 2.10.