Exam 7: Random Variables and Discrete Probability Distributions

If X and Y are random variables with E(X) = 6 and E(Y) = 9, then E(2X + 3Y) is:

A probability distribution for a single random variable is referred to as a(n) ____________________ distribution.

NARRBEGIN: Mobile Phones Sales Mobile Phones Sales After analyzing sales data, the owner of a Mobile Phone store produced the following joint probability distribution of the number of iPhones (X) and Blackberries (Y) sold daily. X 1 1 0.4 0.1 2 0.3 0.2 NARREND -{Mobile Phones Sales Narrative} Find the marginal probability distribution of the number of iPhones sold daily.

NARRBEGIN: Stress Stress Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed.NARREND -{Stress Narrative} Find P(X < 3).

NARRBEGIN: Sports Fans Sports Fans Suppose that past history shows that 5% of college students are sports fans. A sample of 10 students is to be selected.NARREND -{Sports Fans Narrative} Find the probability that less than 1 student is a sports fan.

NARRBEGIN: Golfing Store Golfing Store The joint probability distribution of variables X and Y is shown in the table below, where X is the number of drivers and Y is the number of putters sold daily in a small golfing store. X 1 2 3 1 0.30 0.18 0.12 2 0.15 0.09 0.06 3 0.05 0.03 0.02 NARREND -{Golfing Store Narrative} Find P(Y = 2 | X = 1)

NARRBEGIN: Blackjack Blackjack The probability distribution of a random variable X is shown below, where X represents the amount of money (in $1,000s) gained or lost in a particular game of Blackjack. -4 0 4 8 p(x) 0.15 0.25 0.20 0.40 NARREND -{Blackjack Narrative} Find the following values, and indicate their units. a.E(X) b.V(X) c.Standard deviation of X

NARRBEGIN: Returns on Investment Returns on Investment An analysis of the stock market produces the following information about the returns of two stocks. Stock 1 stock 2 expcted Returns 15\% 18\% Standand Deviations 20 32 Assume that the returns are positively correlated with correlation coefficient of 0.80.NARREND -{Returns on Investment Narrative} Find the standard deviation of the return on a portfolio consisting of an equal investment in each of the two stocks.

Faculty rank (professor, associate professor, assistant professor, and lecturer) is an example of a discrete random variable.

The length of time for which an apartment in a large complex remains vacant is a discrete random variable.

NARRBEGIN: Number of Birds Number of Birds Alana and Eva are sisters. Let X denote the number of birds that Alana may have in the next two years, and let Y denote the number of birds Eva may have during the same period. The marginal probability distributions of X and Y are shown below. 0 1 2 ( ) 0.5 0.3 0.2 y 0 1 2 ( ) 0.4 0.5 0.1 NARREND -{Number of Birds Narrative} Calculate E(X + Y) directly by using the probability distribution of X + Y.

If X and Y are ____________________, the variance of their sum is equal to the sum of their variances.

Which of the following about the binomial distribution is not a true statement?

NARRBEGIN: Sports Fans Sports Fans Suppose that past history shows that 5% of college students are sports fans. A sample of 10 students is to be selected.NARREND -{Sports Fans Narrative} Find the probability that more than 1 student is a sports fan.

If the covariance between two investments of a portfolio is zero, the variance of the portfolio will be equal to the sum of the variances of the investments.

NARRBEGIN: Retries Retries The following table contains the probability distribution for X = the number of retries necessary to successfully transmit a 1024K data package through a double satellite media. 0 1 2 3 ( ) 0.35 0.35 0.25 0.05 NARREND -{Retries Narrative} What is the probability of a least one retry?

NARRBEGIN: Online Bankers Online Bankers An official from the securities commission estimates that 75% of all online bankers have profited from the use of insider information. Assume that 15 online bankers are selected at random from the commission's registry.NARREND -If X has a binomial distribution with n = 4 and p = 0.3, find the probability that X is at least one.

NARRBEGIN: Classified Department Pho Classified Department Phone Calls A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another.NARREND -{Classified Department Phone Calls Narrative} Find the probability that the department will receive seven calls between 2 and 3 P.M. on a particular afternoon.

NARRBEGIN: Gym Visits Gym Visits Let X represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: 0 1 2 3 ( ) 0.05 0.25 0.50 0.20 NARREND -{Gym Visits Narrative} What is the probability that the student visits the gym at most twice in a month?

NARRBEGIN: Stress Stress Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed.NARREND -{Stress Narrative} Find the probability distribution of X.