1) In basketball, one of the possible penalties after a foul is called a free throw. The fouled player gets one shot at the basket from the foul line. If he misses this shot, he is awarded no points and the penalty is over. If he makes the shot, then he gets one point and gets to take another shot. If he makes the second shot he gets an additional point, and the ball is turned over to the other team. If he misses the second shot, the penalty is over. Suppose that the probability of scoring a shot is 60%, and the likelihood of making one shot is independent of the outcome of any other shot. Construct the probability distribution function for the one-and-one penalty? a) On average, how many points would you expect to get from the penalty? b) What is the CV of the distribution?
1) In basketball, one of the possible penalties after a foul is called a free throw. The fouled player gets one shot at the basket from the foul line. If he misses this shot, he is awarded no points and the penalty is over. If he makes the shot, then he gets one point and gets to take another shot. If he makes the second shot he gets an additional point, and the ball is turned over to the other team. If he misses the second shot, the penalty is over. Suppose that the probability of scoring a shot is 60%, and the likelihood of making one shot is independent of the outcome of any other shot. Construct the
a) On average, how many points would you expect to get from the penalty?
b) What is the CV of the distribution?
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