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We will now go through an example that brings together all of the concepts that we have introduced. We have a stick of length l. And we break that stick at some random location, which corresponds to a random variable, X. And we assume that this random variable is uniform over the length of the stick. So its PDF has this particular shape. And for the PDF to integrate to 1, the height of this PDF must be equal to 1 over l. Then we take the piece of the stick that we are left with, which has length X, and we break it at a random location, which we call Y. And we assume that this location Y is uniformly distributed over the length of the stick that we were left with. What does this assumption mean? It means that if the first break was at some particular value, x, then the random variable Y has a conditional distribution, which is uniform over the interval from 0 to x. So the conditional PDF is uniform. A conditional PDF, like any other PDF, must integrate to 1. So the height of this condi