1. A soccer player will kick a ball 80 times during practice.Assume that the kicks are independent of each
other, and the probability that he scores is 0.6 (60% chance thatthe ball goes into the goalpost and 40%
chance that the ball does not go into the goalpost).
Let X be the number of successful goals (number of scores) out ofthe 80 kicks.
(a) What is the distribution of X?
(b) Write the pmf f(x) and name its parameters.
(c) What key assumption of the kicks is needed to determine thisdistribution?
(d) What is the expected number of kicks that go into the goalpost?Interpret this value for the soccer
player (in a sentence or two).
(e) What is the expected number of kicks that do not go into thegoal post? Interpret this value for
the soccer player (in a sentence or two).
(f) Say each kick is blocked by the opponent goal keeper 30% of thetime regardless of whether the ball
was going in or out of the goalpost. What is the expected number ofblocks? What is the variance
of the number of blocks?
(g) Now say each kick that was supposed to go into the goal post isrebounded by another player 50%
of the time and each kick that was not going into the goalpost isrebounded by another player 10%
of the time. What is the expected number of rebounds?