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Hi. In this problem, well get a chance to see the usefulness of conditioning in helping us to calculate quantities that would otherwise be difficult to calculate. Specifically, well be using the law of iterated expectations and the law of total variance. Before we get started, lets just take a quick moment to interpret what these two laws are saying. Really, what its saying is, in order to calculate the expectation or the variance of some random variable x, if thats difficult to do, well instead attack this problem in stages. So the first stage is, well condition on some related random variable, y. And the hope is that by conditioning on this and reducing it to this conditional universe, the expectation of x will be easier to calculate. Now, recall that this conditional expectation is really a random variable, which is a function of the random variable y. So what weve done is we first average out x given some y. What remains is some new random variable, which is a function o