A bag contains r balls, of which 2 are red and r - 2 are black. We draw a ball at random, we write down its color, and we put it to one side (not back in the bag). We repeat the procedure r times.
Let X be the number of draws needed to obtain a red ball, and let Y be the number of draws needed to obtain a second red ball.
a. Find the probability law of the vector (X,Y) , and find its marginals.
b. Evaluate Cov(X,Y) .
Probailities are calculated using appropriate tables and calculations. The solution is detailed.