# Question: Let Zn n 1 be a sequence of random

Let Zn, n ≥ 1, be a sequence of random variables and c a constant such that, for each ε > 0, P{|Zn − c| > ε}→0 as n→∞. Show that, for any bounded continuous function g,

E[g(Zn)]→g(c) as n→∞

E[g(Zn)]→g(c) as n→∞

**View Solution:**## Answer to relevant Questions

Twenty workers are to be assigned to 20 different jobs, one to each job. How many different assignments are possible? Consider the following combinatorial identity: (a) Present a combinatorial argument for this identity by considering a set of n people and determining, in two ways, the number of possible selections of a committee of any ...Let f(x) be a continuous function defined for 0 ≤ x ≤ 1. Consider the functions (called Bernstein polynomials) and prove that Let X1, X2, . . . be independent Bernoulli random variables with mean x. Show that Bn(x) = ...The following algorithm will generate a random permutation of the elements 1, 2, . . . , n. It is somewhat faster than the one presented in Example 1a but is such that no position is fixed until the algorithm ends. In this ...Use the inverse transformation method to present an approach for generating a random variable from the Weibull distributionPost your question