Question

1. Suppose a basketball team makes it into the final four seven times, and that each tournament outcome is independent and they have probability of winning each tournament equal to 0.25. Let the random variable X be the number of wins by this team in seven years.

a. Give the name the distribution family for X and give its parameters.

b. What is the expected value of X (use a formula once you know the distribution family)?

c. What is the variance and standard deviation of X (again use a formula).?

d. What is the probability the team wins 3 or more games? (feel free to use your calculator, R, or an online calculator such as https://gallery.shinyapps.io/dist_calc/)

Answer 1

a) The number of wins in 7 years could be modelled here as a binomial distribution given as:

b) The expected value of the distribution is computed here as:

E(X) = np = 7*0.25 = 1.75

Therefore 1.75 is the required expected value here.

c) The variance and standard deviation are computed here as:

therefore Var(X) = 1.3125

The standard deviation is computed here as:

therefore SD(X) = 1.1456

d) Probability that the team wins 3 or more games is computed here as:

Therefore 0.2436 is the required probability here.