59. An urn contains 30 balls, of which 10 are red and 8 are blue. From this urn, 12 balls are randomly withdrawn. Let *X* denote the number of red, and *Y* the number of blue, balls that are withdrawn. Find Cov(*X*, *Y*)

(a) by defining appropriate indicator (that is, Bernoulli) random variables

*X_i*, *Y_i* such that $X = \sum_{i=1}^{10}X_{i}$, $Y = \sum_{i=1}^{8}Y_{i}$

(b) by conditioning (on either *X* or *Y*) to determine *E[XY]*.

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