STAT312 Lecture : Convergence in probability, Jensen’s inequality.pdf
5 Apr 2014
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Limits and continuity in probability: let { a sequence of r. v. s, e. g. toss a fair coin and let. } be times denote the proportion of heads in the. ] = 1 2 and we also expect tosses. Then to be near 1 2, with high probability, for large. We say that converges to a constant in probability , and write. The weak law of large numbers states that if is the average of independent r. v. s. = 1 0 with probability 1 2 each; = 1 2; by the wlln. This is a basic notion required for the theory of estimation in statistics. 2 of a population is esti- from the pop- mated, via a sample ulation, by the sample variance 2. The wlln: we say can be used to show that, then also. ; this is a consequence of the following. R is ((1 (1 for all on (0. 0 implies function has a derivative then it is convex.
