2. A tennis player will take 20 serves at practice. Assuming that other, and the
ID: 3355657 • Letter: 2
Question
2. A tennis player will take 20 serves at practice. Assuming that other, and the probability that a serve the serve goes out of bounds). the serves are independent of each goes in is 0.85 (85%chance the serve goes in and 15% chance Let X be the number of serves out of the 20 that go in a. What is the distribution of X? b. Write the pmf ((x)), and name its parameters c. What key assumption of the serves is needed to determine this distribution? d. What is the expected number of serves that go in. Interpret this value for the tennis player (in a sentence or two). e. What is the expected number of serves that go out of bounds. Interpret this value for the tennis player (in a sentence or two). f. Say each serve is returned by the other player 60% of the time regardless of whether or not it was going out or in. What is the expected number of returned serves? What is the variance of the number of returned serves? g. Now say each serve that is going in is returned by the other player 85% of the time and each serve that is going out is returned (before the ball bounces) 10% of the time what is the expected number of returned serves?Explanation / Answer
Here the given distribution is binomial distribution where
n = 20 and p = 0.85
(a) Distribution of X is binomial.
(b) Here parameters are n = 20 and p = 0.85
P(X) = 20CX (0.85)X (0.15)20 -X
(c) Here key assumption is taken that each service is independent of each other.
(d) Expected number of serves that go in E(X) = 20 * 0.85 = 17
Here we can say that out of 20 serves, on an average 17 will go in.
(e) Expected number of serves that will go out E(Y) = 20 * 0.15 = 3
Here we can say that out of 20 serves, on an average 3 will go out.
(f) Expected number of return serves if percentage of serves that will be returned when p = 0.60
so E(Z) = 20 * 0.60 = 12
Varaince of number of returned serves = n * p * (1-p) = 20 * 0.60 * 0.40 = 4.8
(g) Here if W is number of returned serves
then
E(W) = 20 * 0.85 * 0.85 + 20 * 0.15 * 0.10 = 14.75
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.