Exam 7: Random Variables and Discrete Probability Distributions

NARRBEGIN: Number of Hamsters 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. X 1 1 0.4 0.1 2 0.3 0.2 NARREND -{Number of Hamsters Narrative} Calculate E(XY).

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 P(X > 1).

The expected number of heads in 100 tosses of an unbiased coin is

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance. The distance a person rides in a year is an example of a(n) ____________________ random variable.

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} Calculate COV(X,Y). Did you expect this answer? Why?

The number of home insurance policy holders is an example of a discrete random variable

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.

Which of the following is not a characteristic of a binomial experiment?

NARRBEGIN: Car Sales 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. 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 -{Car Sales Narrative} Calculate V(X) and V(Y).

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} Compute the mean and variance of X.

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.

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} Find the mean $\mu$ and the standard deviation $\sigma$ of this distribution.

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 -{Online Bankers Narrative} Find the probability that at most 10 have profited from insider information.

NARRBEGIN: Number of Horses Number of Horses The random variable X represents the number of horses per family in a rural area in Iowa, with the probability distribution: p(x) = 0.05x, x = 2, 3, 4, 5, or 6.NARREND -{Number of Horses Narrative} Find the expected number of horses per family.

NARRBEGIN: Number of Hamsters 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. X 1 1 0.4 0.1 2 0.3 0.2 NARREND -{Number of Hamsters Narrative} Calculate all possible values of the conditional probabilities, for X given Y and for Y given X.

To find the probability that X is at most 10, you should find the probability that X is 10 or ____________________.

A function or rule that assigns a numerical value to each simple event of an experiment is called:

NARRBEGIN: Montana Highways 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.NARREND -{Montana Highways Narrative} What is the distribution of X?

In a Poisson distribution, the mean and standard deviation are equal.

In each trial of a binomial experiment, there are ____________________ possible outcomes.