Discrete Probability Distributions

Var(X + Y) =

Var(X) + Var(Y) + 2Cov(X, Y)

Which of the following are examples of a binomial experiment? a. Ask customers how much they spend on an average trip to a grocery store. b. Ask customers at a movie theater if they spent $20 or more on concessions. c. Ask investors if they are risk adverse, risk neutral, or risk loving. d. Ask randomly-selected people whether they are members of Facebook.

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

Generally, a person who is risk neutral

bases decisions solely on the basis of expected values.

In the following scenarios, indicate those that describe a Poisson random variable. a. The number of customers in a sample of 20 who use a credit card to make a purchase at a local pharmacy, b. The number of mortgage applicants who receive a loan in a sample of 10 applicants. c. The number of leaks in a specified stretch of a pipeline. d. The number of customers who purchases concessions over the next hour at a movie theater.

c. The number of leaks in a specified stretch of a pipeline. d. The number of customers who purchases concessions over the next hour at a movie theater.

In order to calculate the variance of the sum of two random variables, we

sum the individual variances plus two times the covariance.

The probability of each value x in a discrete probability distribution is a value between __________ and __________.

0, 1

0! =

1

When calculating a portfolio expected return, the weights must add to what?

1

With a discrete probability distribution, EP(X = xi) =

1

A __________ random variable is defined as the number of successes achieved in the n trials of a Bernoulli process.

Binomial

Which distribution is appropriate when counting the number of successes in n trials if the probability of success p remains constant from trial to trial?

Binomial

A __________ random variable, on the other hand, is characterized by uncountable values in an interval.

Continuous

The P(X =< x) defines the __________ distribution function.

Cumulative

With the discrete uniform distribution, each value is __________ likely.

Equally

Which of the following is the formula for an expected value?

ExiP(X = x)

E(X) is referred to as the __________ __________ of the discrete random variable.

Expected Value

True or false: a discrete random variable X may assume an (infinitely) uncountable number of distinct values.

False (a discrete random variable X assumes a countable number of distinct values, that is, the possible values of X can be listed in a finite or infinite sequences)

A value of the correlation coefficient of zero means there is __________ linear relationship between the variables.

No

A value of the correlation coefficient of zero means there is ___________ linear relationship between the variables.

No

A Poisson random variable describes the number of successes of a certain event

Over a given interval of time or in space.

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

Population Mean

A __________ is a collection of assets.

Portfolio

Every discrete random variable is associated with a

Probability Distribution

In a Poisson process, the probability of success in any interval is __________ to the size of the interval.

Proportional

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.

Both __________ as well as __________ are relevant for evaluating the investment.

Reward, Risk

This consumer demands a positive expected gain as compensation for taking risk.

Risk-Averse

This consumer completely ignores risk and makes his/her decisions solely on the basis of expected gains.

Risk-neutral

With a correlation coefficient, the closer the value is to 1, the __________ is the positive linear relationship between the variables.

Stronger

The discrete uniform distribution has a __________ number of specified values.

Finite

Generally, the higher the positive correlation between assets' returns in a portfolio, the

Greater the risk in the portfolio.

The __________ random variable is the number of successes achieved in the n trials of a two-outcome experiment, where the trials are not assumed to be independent.

Hypergeometric

In a Poisson process, the number of successes counted in nonoverlapping intervals are

Independent

When calculating a portfolio expected return, the larger the investment in A, the __________ the weight of A in the calculations.

Larger

A risk-__________ consumer may be willing to take a risk even if the expected gain is negative.

Loving

Generally, the greater the diversification of a portfolio, then

The lower the correlation among the assets' returns, thus increasing risk.

The standard deviation of a portfolio's return is a measure of

The variability which is synonymous with risk.