4. In basketball game, a player is about to do two free throws. The probability

Question

4. In basketball game, a player is about to do two free throws. The probability that the first free throw is good is 60%. If the player gets the first ball in, he would be relaxed and the chance of a successful second throw improves to 80%. However, if the first shot is missed, the second shot has a success rate of 50%. Observe the number points earned by the player and write down the joint PMF of points earned by this player in two free throws. What is the PMF of the total score earned in two free throws? Find the correlation coefficient of the points earned in two free throws.

Explanation / Answer

let p(x,y) represent the success by 1   and x in first and y in 2nd

p(0,0) = 0.4*0.5 = 0.20

p(1,0)=0.6*0.2 = 0.12

p(0,1)=0.4*0.5=0.20

p(1,1) = 0.6*0.8=0.48

hence

pmf

P(Z =0) = 0.20

P(Z = 1) = 0.12+0.20 = 0.32

P(Z =2) = 0.48

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