Common Probability Distribution Flashcards
A _____ describes the probabilities of all the possible outcomes for a random variable.
Probability distribution
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.
Discrete random variable
A _____ _____ variable is one for which the number of possible outcomes is infinite, even if lower and upper bounds exist.
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.
A _____ _____ _____ variable is one for which the probabilities for all possible outcomes for a discrete random variable are equal.
Discrete uniform random
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.
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%.
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.”
Binomial random
A binomial random variable for which the number of trials is 1 is called a _____ random variable.
Bernoulli
Formula: Binomial Probability Function
Formula: Expected value of a binomial random variable
E(X) = np
Variance of a binomial random variable
X = np(1 − p)
_____ distributions: Distribution of a single random variable
Univariate
_____ distribution: Distribution of a mutliple random variables
Multivariate
There are (formula) pairs of correlations in a multivariate distribution
0.5n(n − 1)
_____ _____ is a range of values around the expected outcome within which we expect the actual outcome to be some specified percentage of the time.
Confidence interval
The 90% confidence interval for X is X − _____s to X + _____s.
1.65
The 95% confidence interval for X is X − _____s to X + _____s.
1.96
The 99% confidence interval for X is X − _____s to X + _____s.
2.58
The _____ _____ distribution is a normal distribution that has been standardized so that it has a mean of zero and a standard deviation of 1.
Standard normal
_____ _____ is the probability that a portfolio value or return will fall below a particular (target) value or return over a given time period.
Shortfall risk
_____ criterion states that the optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable level (threshold level).
Roy’s safety-first
Formula: Z-score
Formula: Safety-first Ratio
The _____ distribution is used to model price relatives
Lognormal distribution
_____ _____ returns are just the compound returns we are familiar with, given some discrete compounding period, such as semiannual or quarterly.
Discretely compounded
Formula: Continuous compounding-to-EAR
Formula: Holding period return (HPR)-to-Continuously compounded rate(Rcc)
Formula: Holding period return after t years, when continuously compounded
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 _____.
T-distribution
Number of degrees of freedom of a t-distribution, for sample mean
n-1
The t-distribution has _____ tails that the normal distribution.
Fatter
T-distribution: As the degrees of freedom (the sample size) gets _____, the shape of the t-distribution more closely approaches a standard normal distribution.
Larger
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.
Greater
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).
Wider
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.
Chi-square
As degrees of freedom get _____, the chi-square distribution approaches the normal distribution in shape.
Larger
The _____ distribution is often used in tests of the value of the variance of a normally distributed population.
Chi-square
The _____ distribution is the distribution of the quotient of two (appropriately scaled) independent chi-square variables
F
Common use of the _____ distribution is to determine the probability that the variances of two independent normal distributions are equal
F
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.
Monte Carlo simulation
