Exam 5: Discrete Probability Distributions

Thirty percent of the CFA candidates have a degree in economics.A random sample of three CFA candidates is selected.What is the probability that none of them has a degree in economics?

Exhibit 5-4.Consider the following probability distribution. Refer to Exhibit 5-4.The variance is _____.

Exhibit 5-2.Consider the following cumulative distribution function for the discrete random variable X. Refer to Exhibit 5-2.What is the probability that X equals 2?

Exhibit 5-11.For a particular clothing store,a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed.Suppose six customers are randomly selected and are mailed $10-off coupons. Refer to Exhibit 5-11.What is the expected number of coupons that will be redeemed?

Exhibit 5-14.The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005. Refer to Exhibit 5-14.What is the probability that no more than two foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?

Which of the following can be represented by a discrete random variable?

A car salesman has a 5% chance of landing a sale with a random customer on his lot.Suppose 10 people come on the lot today. A)What is the probability that he sells exactly three cars today? B)What is the probability he sells less than two cars today? C)What is the expected number of cars he is going to sell today?

Exhibit 5-3.Consider the following probability distribution. Refer to Exhibit 5-3.The variance is ____.

Exhibit 5-15.A bank manager estimates that an average of two customers enter the tellers' queue every five minutes.Assume that the number of customers that enter the tellers' queue is Poisson-distributed. Refer to Exhibit 5-15.What is the probability that less than two customers enter the queue in a randomly selected five-minute period?

Exhibit 5-16.According to geologists,the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. Refer to Exhibit 5-16.What is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?

Which of the following can be represented by a discrete random variable?

We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size N is significantly larger than the sample size n.

Exhibit 5-3.Consider the following probability distribution. Refer to Exhibit 5-3.The expected value is ___.

An analyst estimates that the year-end price of a stock has the following probabilities: The stock's expected price at the end of the year is _______.

Exhibit 5-13.Chauncey Billups,a current shooting guard for the Los Angeles Clippers,has a career free-throw percentage of 89.4%.Suppose he shoots six free throws in tonight's game. Refer to Exhibit 5-13.What is the probability that Billups makes five or more of his free throws?

Exhibit 5-17.Suppose a baseball team has 14 players on the roster who are not members of the pitching staff.Of those 14 players,assume that 3 have recently taken a performance-enhancing drug.Suppose the league decides to randomly test five members of the team. Refer to Exhibit 5-17.What is the probability that at least one of the tested players is found to have taken a performance-enhancing drug?

Exhibit 5-14.The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States,but even when analysis is restricted to relatively strong housing markets the numbers are staggering.For example,in 2011 an average of three residential properties were auctioned off each weekday in the city of Boston,up from an average of one per week in 2005. Refer to Exhibit 5-14.What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2011?

Exhibit 5-10.According to a study by the Centers for Disease Control and Prevention,about 33% of U.S.births are Caesarean deliveries (National Vital Statistics Report,Volume 60,Number 2,November 2011).Suppose seven expectant mothers are randomly selected. Refer to Exhibit 5-10.The expected number of mothers who will not have a Caesarean delivery is ______.

A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

Exhibit 5-3.Consider the following probability distribution. Refer to Exhibit 5-3.The standard deviation is _________.