Kevin Durant and Russell Westbrook are in a team 3 point shooting contest representing the Oklahoma City Thunder. They will alternate 3 point attempts and will continue to shoot until they miss a shot - ie when Kevin Durant misses he stops and when Russell Westbrook misses he stops. The random variable of interest is W = total number of successful shots (ie adding successful shots for both players together). Suppose that the events score/miss are independent across shots and across the two players and that the constant probability that Durant scores on any shot is 0.3 while for Westbrook it is 0.4. Denote w for a possible value for W and note that w can be any non-negative integer - ie: 0,1,2,3,......
a) Give an expression for W in terms of two different (though possibly the same type) and independent random variables whose probability mass function is known (ie: consider the special distributions considered in class)
b) Find the value of the probability function PW (w) for w=0,1,2.
c) Find the probability function for the general value w.