Exam 7: Random Variables and Discrete Probability Distributions

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

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. -{Shopping Outlet Narrative} Use the laws of expected value to calculate the mean of Y from the probability distribution of X.

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. -{Number of Horses Narrative} Express the probability distribution in tabular form.

For a random variable X, if V(cX) = 4V(X), where V refers to the variance, then c must be 2.

Which of the following about the binomial distribution is not a true statement?

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

The amount of time that a microcomputer is used per week is an example of a(n) ____________________ random variable.

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} Develop the probability distribution of X + Y.

The covariance between two investments of a portfolio is equal to the sum of the variances of the investments.

The number of homeless people in Boston is an example of a discrete random variable.

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

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 P(X < 3).

The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

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

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 net profit from your investment of $2,000.

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. -{Shopping Outlet Narrative} What did you notice about the mean, variance, and standard deviation of Y = 2X + 1 in terms of the mean, variance, and standard deviation of X?

The mean of a Poisson distribution, where $\mu$ is the average number of successes occurring in a specified interval, is $\mu$ .

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.

The standard deviation of a binomial random variable X is given by the formula $\sigma$ ² = np(1- p), where n is the number of trials, and p is the probability of success.

A community college has 150 word processors.The probability that any one of them will require repair on a given day is 0.025.To find the probability that exactly 25 of the word processors will require repair, one will use what type of probability distribution?