Exam 5: Discrete Probability Distributions

An analyst estimates that a stock has the following probabilities of year-end prices. a.Calculate the expected price at year-end. B)Calculate the variance and the standard deviation.

An analyst believes that a stock's return depends on the state of the economy,for which she has estimated the following probabilities: According to the analyst's estimates,the expected return of the stock is ____.

Lisa is in a free-throw shooting contest where each contestant attempts 10 free throws.On average,Lisa makes 77% of the free throws she attempts. A)What is the probability that she makes exactly eight free throws? B)What is the probability she makes at least nine free throws? C)What is the probability she makes less than nine free throws? D)Lisa is competing against Bill to see who can make the most free throws in 10 attempts.Suppose Bill goes first and makes seven.Should we expect Lisa to make at least as many as Bill? Explain.

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 exactly two of the tested players are found to have taken a performance-enhancing drug?

What is a characteristic of the mass function of a discrete random variable X?

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 probability that three of the customers redeem the coupon?

A cumulative probability distribution of a random variable X is the probability P(X = x),where X is equal to a particular value x.

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 standard deviation of the number of free throws that Billups will make?

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 all six free throws?

Exhibit 5-6.The number of cars sold by a car salesman during each of the last 25 weeks is the following: Refer to Exhibit 5-6.What is the standard deviation of the number of cars sold by the salesman during a week?

A plane taking off from an airport in New York can expect to run into a flock of birds once out of every 1,250 take-offs. A)What is the expected number of bird strikes for 10,000 take-offs? B)What is the standard deviation of the number of bird strikes for 10,000 take-offs? C)What is the probability of running into seven flocks of birds in 10,000 take-offs?

A Poisson random variable counts the number of successes (occurrences of a certain event)over a given interval of time or space.

You have inherited a lottery ticket that may be a $5,000 winner.You have a 35% chance of winning the $5,000 and a 65% chance of winning $0.You have an opportunity to sell the lottery for $1500.What should you do if are risk neutral?

Exhibit 5-6.The number of cars sold by a car salesman during each of the last 25 weeks is the following: Refer to Exhibit 5-6.What is the probability that the salesman will sell one car during a week?

Exhibit 5-18.There are currently 18 pit bulls at the pound.Of the 18 pit bulls,four have attacked another dog in the last year.Joe,a member of the staff,randomly selects six of the pit bulls for his group. Refer to Exhibit 5-18.What is the probability that exactly one of the pit bulls in Joe's group attacked another dog last year?

Exhibit 5-1.Consider the following discrete probability distribution. Refer to Exhibit 5-1.What is the probability that X is greater than 0?

Exhibit 5-9.On a particular production line,the likelihood that a light bulb is defective is 5%.Ten light bulbs are randomly selected. Refer to Exhibit 5-9.What is the probability that none of the light bulbs will be defective?

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 exactly four foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?

The expected value of a random variable X can be referred to as the population mean.

Exhibit 5-1.Consider the following discrete probability distribution. Refer to Exhibit 5-1.What is the probability that X is negative?