Exam 7: Random Variables and Discrete Probability Distributions

Car Sales The joint probability distribution of variables X and Y is shown in the table below.Rebecca and Rachel are car salespeople.Let X denote the number of cars that Rebecca will sell in a month, and let Y denote the number of cars Rachel will sell in a month. -{Car Sales Narrative} Verify that E(X + Y) = E(X) + E(Y).

The covariance of two variables X and Y:

Number of Hamsters The joint probability distribution of X and Y is shown in the accompanying table, where X denotes the number of hamsters that Quinn may have next year, and Y denotes the number of hamsters that her boyfriend, Jason, may have when she moves in with him next year. -{Number of Hamsters Narrative} Compute the covariance and the coefficient of correlation.

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

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. -{Retries Narrative} What is the mean or expected value for the number of retries?

For each of the following random variables, indicate whether the variable is discrete or continuous, and specify the possible values that it can assume. a. X = the number of traffic accidents in Albuquerque on a given day. b. X = the amount of weight lost in a month by a randomly selected dieter. c. X = the average number of children per family in a random sample of 175 families. d. X = the number of households out of 10 surveyed that own a convection oven. e. X = the time in minutes required to obtain service in a restaurant.

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. -{Stress Narrative} Find the probability distribution of X.

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. -{Classified Department Phone Calls Narrative} Find the probability that the department will receive 13 calls between 2 and 4 P.M.on a particular afternoon.

The binomial probability distribution is a discrete probability distribution.

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. -{Mobile Phones Sales Narrative} Calculate V(X + Y) directly by using the probability distribution of X + Y.

A(n) ____________________ random variable is one whose values are uncountable.

In the notation below, X is the random variable, E and V refer to the expected value and variance, respectively.Which of the following is false?

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. -{Online Bankers Narrative} Find the probability that all 15 have profited from insider information.

If X and Y are two variables with , , and COV(X, Y) = 11.76, then the coefficient of correlation = 0.8.

If X and Y are independent random variables, which of the following identities is false?

If X and Y are independent variables, then COV(X, Y) > 0.

A table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities, is called a(n):

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: -{Gym Visits Narrative} Find the mean and the standard deviation of Y = 2X - 1.

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. -{Unsafe Levels of Radioactivity Narrative} Find the probability that there will be no more than 1 incident in a year.