Common Probability Distribution

Question 1

A _____ describes the probabilities of all the possible outcomes for a random variable.

Answer 1

Probability distribution

Question 2

A _____ is one for which the number of possible outcomes can be counted, and for each possible outcome, there is a measurable and positive probability.

Answer 2

Discrete random variable

Question 3

A _____ _____ variable is one for which the number of possible outcomes is infinite, even if lower and upper bounds exist.

Answer 3

Continuous random

Ex: Daily rainfall can be measured in inches, half inches, quarter inches, thousandths of inches, or even smaller increments. Thus, the number of possible daily rainfall amounts between zero and 100 inches is essentially infinite.

Question 4

A _____ _____ _____ variable is one for which the probabilities for all possible outcomes for a discrete random variable are equal.

Answer 4

Discrete uniform random

Question 5

The _____ _____ distribution is defined over a range that spans between some lower limit, a, and some upper limit, b, which serve as the parameters of the distribution.

Answer 5

Continuous uniform

Simple. The probability of outcomes in a range that is one-half the whole range is 50%. The probability of outcomes in a range that is one-quarter as large as the whole possible range is 25%.

Question 6

A _____ _____ variable may be defined as the number of “successes” in a given number of trials, whereby the outcome can be either “success” or “failure.”

Answer 6

Binomial random

Question 7

A binomial random variable for which the number of trials is 1 is called a _____ random variable.

Answer 7

Bernoulli

Question 8

Formula: Binomial Probability Function

Answer 8

Question 9

Formula: Expected value of a binomial random variable

Answer 9

E(X) = np

Question 10

Variance of a binomial random variable

Answer 10

X = np(1 − p)

Question 11

_____ distributions: Distribution of a single random variable

Answer 11

Univariate

Question 12

_____ distribution: Distribution of a mutliple random variables

Answer 12

Multivariate

Question 13

There are (formula) pairs of correlations in a multivariate distribution

Answer 13

0.5n(n − 1)

Question 14

_____ _____ is a range of values around the expected outcome within which we expect the actual outcome to be some specified percentage of the time.

Answer 14

Confidence interval

Question 15

The 90% confidence interval for X is X − _____s to X + _____s.

Answer 15

1.65

Question 16

The 95% confidence interval for X is X − _____s to X + _____s.

Answer 16

1.96

Question 17

The 99% confidence interval for X is X − _____s to X + _____s.

Answer 17

2.58

Question 18

The _____ _____ distribution is a normal distribution that has been standardized so that it has a mean of zero and a standard deviation of 1.

Answer 18

Standard normal

Question 19

_____ _____ is the probability that a portfolio value or return will fall below a particular (target) value or return over a given time period.

Answer 19

Shortfall risk

Question 20

_____ criterion states that the optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable level (threshold level).

Answer 20

Roy’s safety-first

Question 21

Formula: Z-score

Answer 21

Question 22

Formula: Safety-first Ratio

Answer 22

Question 23

The _____ distribution is used to model price relatives

Answer 23

Lognormal distribution

Question 24

_____ _____ returns are just the compound returns we are familiar with, given some discrete compounding period, such as semiannual or quarterly.

Answer 24

Discretely compounded

Question 25

Formula: Continuous compounding-to-EAR

Answer 25

Question 26

Formula: Holding period return (HPR)-to-Continuously compounded rate(Rcc)

Answer 26

Question 27

Formula: Holding period return after t years, when continuously compounded

Answer 27

Question 28

The appropriate distribution to use when constructing confidence intervals based on small samples (n < 30) from populations with unknown variance and a normal, or approximately normal, distribution is the _____.

Answer 28

T-distribution

Question 29

Number of degrees of freedom of a t-distribution, for sample mean

Answer 29

n-1

Question 30

The t-distribution has _____ tails that the normal distribution.

Answer 30

Fatter

Question 31

T-distribution: As the degrees of freedom (the sample size) gets _____, the shape of the t-distribution more closely approaches a standard normal distribution.

Answer 31

Larger

Question 32

The _____ the degrees of freedom, the greater the percentage of observations near the center of the distribution and the lower the percentage of observations in the tails.

Answer 32

Greater

Question 33

The confidence intervals for a random variable that follows a t-distribution is _____ when the degrees of freedom are less for a given significance level (curve is flatter).

Answer 33

Wider

Question 34

The _____ distribution is the distribution of the sum of the squared values of n random variables, and k, the degrees of freedom, is equal to n – 1.

Answer 34

Chi-square

Question 35

As degrees of freedom get _____, the chi-square distribution approaches the normal distribution in shape.

Answer 35

Larger

Question 36

The _____ distribution is often used in tests of the value of the variance of a normally distributed population.

Answer 36

Chi-square

Question 37

The _____ distribution is the distribution of the quotient of two (appropriately scaled) independent chi-square variables

Answer 37

F

Question 38

Common use of the _____ distribution is to determine the probability that the variances of two independent normal distributions are equal

Answer 38

F

Question 39

The _____ is a technique based on the repeated generation of one or more risk factors that affect security values, in order to generate a distribution of security values.

Answer 39

Monte Carlo simulation