# Question: Prove that if E Y X x E Y for all

Prove that if E[Y|X = x] = E[Y] for all x, then X and Y are uncorrelated; give a counterexample to show that the converse is not true.

Prove and use the fact that E[XY] = E[XE[Y|X]].

Prove and use the fact that E[XY] = E[XE[Y|X]].

## Relevant Questions

Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X] = 1.8, what is (a) The largest possible value of P{X = 3}? (b) The smallest possible value ...One ball at a time is randomly selected from an urn containing a white and b black balls until all of the remaining balls are of the same color. Let Ma,b denote the expected number of balls left in the urn when the ...We have 100 components that we will put in use in a sequential fashion. That is, component 1 is initially put in use, and upon failure, it is replaced by component 2, which is itself replaced upon failure by component 3, and ...Use the central limit theorem to solve part (c) of Problem 2. Part (c) of Problem 2 How many students would have to take the examination to ensure, with probability at least .9, that the class average would be within 5 of ...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→∞Post your question