Exam 7: Random Variables and Discrete Probability Distributions

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.

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 13 calls between 2 and 4 P.M. on a particular afternoon.

The variance of a binomial distribution is equal to ____________________.

The variance of a portfolio of two investments will be equal to the sum of the variances of the two investments plus twice the covariance between the investments.

Which of the following is a continuous random variable?

A statistical measure of the strength of the relationship between two random variables X and Y is referred to as the:

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance. How long a person has been a licensed rider is an example of a(n) ____________________ random variable.

A continuous variable may take on any value within its relevant range even though the measurement device may not be precise enough to record it.

NARRBEGIN: Number of Motorcycles 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. 0 1 2 3 ( ) 0.25 0.40 0.20 0.15 NARREND -{Number of Motorcycles Narrative} Find the standard deviation of X.

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 at least five calls between 2 and 4 P.M. on a particular afternoon.

A binomial experiment consists of a(n) ____________________ number of trials, n.

NARRBEGIN: Unsafe Levels of Radioact 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.NARREND -{Unsafe Levels of Radioactivity Narrative} Find the standard deviation of the number of incidents is in one year.

The covariance of two variables X and Y:

NARRBEGIN: Risky Undertaking 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.NARREND -{Risky Undertaking Narrative} If you invest $6,000 in the risky undertaking instead of $2,000, and the possible payoffs triple accordingly, what are the expected value of the net profit from the $6,000 investment?

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

If you add two single probability distributions together you get a bivariate distribution.

For a random variable X, V(X + 3) = V(X + 6), where V refers to the variance.

The expected return of a two-asset portfolio is equal to the product of the weight assigned to the first asset and the expected return of the first asset plus the product of the weight assigned to the second asset and the expected return of the second asset.

The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:

If n = 10 and p = 0.60, then the mean of the binomial distribution is