Question

Steph Curry (a basketball player) can make a free throw 93% of the time. Furthermore, assume that a sequence of free-throw shooting can be thought of as independent Bernoulli trials. Let X = the minimum number of free throws that this player must attempt to make a total of ten shots. What is the PMF of X? What is the probability that the player must attempt 12 shots in order to make ten? What is the expected value and variance of X? a. b. c. 65

Answer 1

a) here this is negative binomial distirbution with paramter r=10 and p=0.93

pmf of X =$\dpi{80} \binom{x-1}{9}(0.93)^{10}(0.07)^{x-10}$

b) P(X=12) =$\dpi{80} \binom{11}{9}(0.93)^{10}(0.07)^{2}$ =0.1304

c) expected value =r/p=10/0.93=10.75

and variance =r*(1-p)/p² =0.8093