Discrete Probability Distributions

Flashcards covering key vocabulary and concepts about discrete probability distributions.

Discrete Random Variables

A variable that can take on a finite number of values, each with an associated probability.

Mutually Exclusive Events

Events that cannot occur at the same time.

Collectively Exhaustive Events

A set of events that covers all possible outcomes.

Binomial Distribution

A probability distribution used to calculate the likelihood of a number of events occurring in a fixed number of trials.

Fixed Number of Trials (n)

The number of times an experiment is conducted in a binomial distribution.

Constant Probability (π)

The same probability of success for each trial in a binomial distribution.

Independent Observations

The outcome of one trial does not affect the outcome of another.

Poisson Distribution

A probability distribution used for counting the number of occurrences of an event in a given time or space.

λ (lambda)

The average number of events in a Poisson distribution within a given window.

Hypergeometric Distribution

A probability distribution similar to binomial used for sampling without replacement from a finite population.

Dependent Trials

Outcomes of trials that are influenced by previous trials.

Covariance

A measure of the strength of the linear relationship between two random variables.

Positive Covariance

Indicates a positive relationship between two variables.

Negative Covariance

Indicates a negative relationship between two variables.

Covariance Formula

Cov(OXY) = Σ P(xi, Y₁) (x₁ - E(X))(y₁ - E(Y)).

Expected Value of Random Variables

The average of all possible outcomes of a random variable.

Variance

A measure of the spread of a set of values; the average of the squared differences from the mean.

Standard Deviation

The square root of the variance, indicating the average distance from the mean.

Weighted Sum of Asset Returns

The total return of a portfolio calculated by multiplying each asset's return by its weight.

Portfolio Return

The total return on an investment portfolio based on the individual asset returns.

E(wX + (1 - w)Y)

Formula representing the expected return of a portfolio of two assets.

Var(wX + (1 − w)Y)

Formula for the variance of a portfolio return that accounts for asset correlation.

Independent Events

Events where the occurrence of one does not affect the occurrence of another.

Summation Notation

A way to represent the summation of a series of terms in statistics.

Count Data

Data that represents the number of occurrences of an event.

Continuous Interval

A range of values in which every point is included without gaps.

Probability Distribution Function

A function that describes the likelihood of obtaining the possible values that a random variable can take.