Exam 7: Random Variables and Discrete Probability Distributions

The Poisson random variable is a:

The following information regarding a portfolio of two stocks are given: w₁ = .65, w₂ = .35, E(R₁) = .12, and E(R₂) = .14.Which of the following regarding the portfolio expected return, E(R_p), is correct?

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.

Let X be a Poisson random variable with $\mu$ = 8.Use the table of Poisson probabilities to calculate: a. P(X $\le$ 6) b. P(X = 4) c. P(X $\ge$ 3) d. P(9 $\le$ X $\le$ 14)

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

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

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 E(X) and E(Y).

If X and Y are independent variables with V(X) = 23.48 and V(Y) = 36.52, then the standard deviation of W = X + Y is $\sigma$ _w = 7.746.

If X and Y are any random variables with E(X) = 5, E(Y) = 6, E(XY) = 21, V(X) = 9 and V(Y) = 10, then the relationship between X and Y is a:

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 at least 3 incidents in a year.

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. -{Golfing Store Narrative} Calculate E(XY).

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. -{Golfing Store Narrative} Calculate COV(X,Y).Did you expect this answer? Why?

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 the standard deviation of number of vehicles that are traveling on Montana highways and exceeding the speed limit.

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 coefficient of correlation between X and Y.Did you expect this result? Why?

Another name for the mean of a probability distribution is its expected value.

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} Compare V(X) + V(Y) to V(X + Y).What is your conclusion?

In a(n) ____________________ experiment, the probability of a success in an interval is the same for all equal-sized intervals.

Returns on Investment An analysis of the stock market produces the following information about the returns of two stocks. Assume that the returns are positively correlated with correlation coefficient of 0.80. -{Returns on Investment Narrative} Find the mean of the return on a portfolio consisting of an equal investment in each of the two stocks.

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

The number of accidents that occur at a busy intersection in one month is an example of a Poisson random variable.