STA305H1 Lecture Notes - Lecture 6: Random Variable, Thai Baht, Subsequence

• School: UTSG
• Department: Statistical Sciences
• Course: STA305H1
• Professor: Nathan Taback

Document Summary

Note: in this section (and subsequently), all random variables are real-valued unless other- wise speci ed. > 0, p x) if, for each lim n . P (|xn x| > ) = 0. {xn} converges to x in r-th mean (xn. E[|xn x|r] = 0. (this type of convergence is also known as lr convergence. ) {xn} converges in distribution to x (xn d x) if lim n . P (xn x) = p (x x) for all x where p (x = x) = 0. Notes: convergence in probability of {xn} to x means that when n is su ciently large, the random variable xn is well-approximated by the random variable x. The limiting p x with p (x = a) = 1 then random variable x is often a constant and so if xn. Almost sure convergence is important in probability theory and more advanced statis- tical theory, but we will not use it in this course.