ORMS 3310 Chapter 5

For a discrete probability distribution, which best describes the probability of each value x?

0 ≤ P(X = x) ≤ 1

Generally, a person who is risk averse

demands a reward for taking risk.

What are the two key properties of a discrete probability distribution?

0 ≤ P(X = x) ≤ 1 and ∑P(X=xi)∑P(X=xi) = 1

A discrete random variable X may assume an

a countable number of distinct values.

The expected value for any discrete random variable is found by summing up the product of the values of the random variables and their respective probabilities. This can be simplified for the binomial random variable by

dividing the probability of a success by the number of trials. Reason: E(X)=np.

The variance for any discrete random variable is found by weighting the squared deviations about the mean by the respective probabilities. This can be simplified for the binomial random variable by

multiplying the number of trials by the probability of a success and the probability of a failure.

The sum of the probabilities of all possible x values in a discrete distribution equals what?

1

Which of the following are examples of a binomial experiment?

Ask 27 customers at a movie theater if they spent $20 or more on concessions. Ask 12 randomly-selected people whether they are members of Facebook.

All of the following are conditions of a binomial experiment (Bernoulli process) EXCEPT:

For each trial, the probability of a 'success' equals the probability of a 'failure'. Reason: This implies that the probability of 'success' is 0.50 and the probability of 'failure' is 0.50. This is not a necessary condition.

A cumulative distribution function explicitly displays

P(X≤x).

Suppose the expected value of a risky transaction is $1,000 and the value of a no-risk transaction is also $1,000. What type of consumers would be willing to engage in the risky transaction?

Risk neutral.

The binomial formula consists of three parts. Which one of the following is not part of the formula?

The conditional probability of a success given a failure. Reason: Trials are independent -- so, conditional probabilities aren't needed.

All of the following are features of a discrete uniform distribution EXCEPT

The distribution is bell-shaped. Reason: Since each value of a discrete uniform distribution is equally likely, the distribution is "flat" instead of bell-shaped.

Which of the following are true about f a binomial random variable? Select all that apply.

The mean must be between 0 and n. The mean may be a value that is not possible for the random variable.

Which of the following are examples of discrete random variables?

The number of bedrooms in a randomly selected house. The number of students who earn an "A" on their statistics exam

Which of the following can be represented by a discrete random variable?

The number of defective light bulbs in a sample of five bulbs Reason: This discrete variable X can assume the possible values 0, 1, 2, 3, 4, 5.

Since there are only two outcomes, 'success' and 'failure,' what must be true about their probabilities?

The probabilities must add to one. Reason: They must add to one since one of the events are complements.

The expected value of the discrete random variable X is

a weighted average of all possible values of X.

Let X = the side showing when a die is rolled. X is assumed to follow a uniform distribution because

each value of X has the same probability.

The variance for probability distribution measures spread around the

mean.

The expected value of a distribution is also referred to as the

population mean.

The probability distribution that describes a discrete random variable is called a

probability mass function.

A function that assigns numerical values to the outcomes of a random experiment is called a

random variable

When calculating the probability of x successes in n trials of a binomial experiment, the probability of success and the probability of failure

remain the same, even when a probability is calculated for a different value of x.

When calculating the variance and standard deviation for a discrete random variable, the squared differences about the mean are

weighted by the probabilities of each value.

For a discrete random variable, the variance of X is calculated as

∑(xi−μ)2P(X=xi)