Suppose a ball is thrown upward at time t = 0 with initial height X and initial upward velocity Y, such that X and Y are independent, exponentially distributed with parameter A. The height at time t is thus H(t) = X + Yt, where c is the gravitational constant. Let T denote the time the ball reaches its maximum height and M denote the maximum height. Find the joint pdf of T and M, fT,M(a, B).

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