Consider the joint probability distribution shown in the table below. The numbers in the cells are the values of p(x, y) corresponding to pairs of values of the discrete random variables X and Y, for X = 1, 2, 3 and Y = 0, 1, 2. In a flexible manufacturing system, X represents the number of machines available, and Y represents the number of sequential operations required to process a part.

Find the marginal probability distribution p(x) for the discrete random variable X. Find the expected value of the conditional probability of Y given X = 2.

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