An urn contains 30 balls, of which 10 are red and 8 are blue. From this urn, 12 balls are...

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 From this urn, 12 balls are randomly withdrawn. Let X denote the number of red and Y the number of blue balls that are withdrawn.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

 such that

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