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} Calculate V(X)and V(Y).

In a Poisson distribution,the:

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.

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} Determine the marginal probability distribution of Y.

The ____________________ of X and Y is one measure of the strength and direction of the linear relationship between X and Y.However this number is hard to put into perspective.

If X has a binomial distribution with n = 4 and p = 0.3,find the probability that X is at most one.

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. ​ ​ -{Number of Birds Narrative} Calculate E(X + Y)directly by using the probability distribution of X + Y.

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 at least 6 have profited from insider information.

Which of the following regarding the mean and variance of a portfolio of k stocks is false?

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. ​ ​ -{Number of Birds Narrative} Compute the mean and variance of X.

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

In a Poisson experiment,the probability of a success in an interval is ____________________ to the size of the interval.

Risky Undertaking ​ Suppose you make a $2,000 investment in a risky undertaking.There is a 50% chance that the payoff from the investment will be $5,000,a 20% chance that you will just get your money back,and a 30% chance that you will receive nothing at all from your investment. ​ ​ -{Risky Undertaking Narrative} Find the expected value of the payoff from your investment of $2,000.

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. ​ ​ -{Number of Birds Narrative} Calculate E(XY)directly by using the probability distribution of XY.

Number of Motorcycles The probability distribution of a discrete random variable X is shown below,where X represents the number of motorcycles owned by a family. ​ ​ -{Number of Motorcycles Narrative} Find the expected value of X.

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} Calculate all possible values of the conditional probabilities,for X given Y and for Y given X.

If X and Y are two variables with ,and COV(X,Y)= 14.703,then the coefficient of correlation ρ = 0.78.

Number of Motorcycles The probability distribution of a discrete random variable X is shown below,where X represents the number of motorcycles owned by a family. ​ ​ -{Number of Motorcycles Narrative} Find the standard deviation of X.

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways,where speed limits are posted at 70 miles per hour,were exceeding the limit.Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour.Let X denote the number of vehicles that were exceeding the limit. ​ ​ -{Montana Highways Narrative} Find P(X = 2).

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} Calculate V(X + Y)directly by using the probability distribution of X + Y.