Probability Distributions Study Cards

Enhance Your Learning with Probability Distributions Flash Cards for quick learning



Discrete Probability Distributions

Probability distributions that can only take on a countable number of values, such as the binomial distribution and the Poisson distribution.

Continuous Probability Distributions

Probability distributions that can take on any value within a specified range, such as the normal distribution and the exponential distribution.

Binomial Distribution

A discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Poisson Distribution

A discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

Normal Distribution

A continuous probability distribution that is symmetric and bell-shaped, commonly used to model real-valued random variables.

Exponential Distribution

A continuous probability distribution that models the time between events in a Poisson process, such as the time between phone calls at a call center.

Uniform Distribution

A continuous probability distribution that models outcomes that are equally likely over a specified range, such as rolling a fair die.

Gamma Distribution

A continuous probability distribution that generalizes the exponential distribution and is used to model the waiting time until a specified number of events occur.

Beta Distribution

A continuous probability distribution that models random variables that are constrained to the interval [0, 1], such as the probability of success in a binomial distribution.

Chi-Square Distribution

A continuous probability distribution that arises in the context of hypothesis testing and is used to model the sum of squared standard normal deviates.

Student's t-Distribution

A continuous probability distribution that arises in the context of hypothesis testing when the sample size is small and the population standard deviation is unknown.

F-Distribution

A continuous probability distribution that arises in the context of hypothesis testing and is used to compare the variances of two independent normal populations.

Multinomial Distribution

A discrete probability distribution that generalizes the binomial distribution to more than two possible outcomes, such as rolling a fair die multiple times.

Hypergeometric Distribution

A discrete probability distribution that models the number of successes in a fixed number of draws without replacement from a finite population.

Negative Binomial Distribution

A discrete probability distribution that models the number of failures that occur before a specified number of successes in a sequence of independent Bernoulli trials.

Geometric Distribution

A discrete probability distribution that models the number of trials needed to achieve the first success in a sequence of independent Bernoulli trials.

Log-Normal Distribution

A continuous probability distribution that models random variables whose logarithm is normally distributed, often used to model positive-valued variables that are skewed to the right.

Weibull Distribution

A continuous probability distribution that models the time until a specified event occurs, often used to model failure times in reliability engineering.

Pareto Distribution

A continuous probability distribution that models the distribution of wealth or income, characterized by a heavy tail and a high concentration of small values.

Triangular Distribution

A continuous probability distribution that models random variables that are constrained to a specified range and have a triangular shape, often used in simulation studies.

Uniform Discrete Distribution

A discrete probability distribution that models outcomes that are equally likely over a specified range of integers, such as rolling a fair die.

Bernoulli Distribution

A discrete probability distribution that models a single trial with two possible outcomes, often used to model success or failure.

Geometric Negative Hypergeometric Distribution

A discrete probability distribution that models the number of trials needed to achieve the first success in a sequence of dependent Bernoulli trials without replacement.

Hyperexponential Distribution

A continuous probability distribution that models the time between events in a non-homogeneous Poisson process, where the rate of occurrence changes over time.

Hypergeometric Negative Binomial Distribution

A discrete probability distribution that models the number of failures that occur before a specified number of successes in a sequence of dependent Bernoulli trials without replacement.

Inverse Gaussian Distribution

A continuous probability distribution that models random variables that are positive-valued and skewed to the right, often used to model time-to-failure data.

Laplace Distribution

A continuous probability distribution that models random variables that are symmetric and have heavy tails, often used to model noise or outliers in data.

Logistic Distribution

A continuous probability distribution that models random variables that are symmetric and have S-shaped tails, often used to model growth or logistic regression.

Loglogistic Distribution

A continuous probability distribution that models random variables that are positive-valued and have S-shaped tails, often used to model survival or reliability data.

Negative Hypergeometric Distribution

A discrete probability distribution that models the number of successes in a fixed number of draws without replacement from an infinite population.

Noncentral Beta Distribution

A continuous probability distribution that models random variables that are constrained to the interval [0, 1] and have a non-zero skewness, often used in Bayesian statistics.

Noncentral Chi-Square Distribution

A continuous probability distribution that arises in the context of hypothesis testing when the null hypothesis is not true, often used in analysis of variance (ANOVA).

Noncentral F-Distribution

A continuous probability distribution that arises in the context of hypothesis testing when the null hypothesis is not true and the variances of the populations are unequal, often used in analysis of variance (ANOVA).

Noncentral Student's t-Distribution

A continuous probability distribution that arises in the context of hypothesis testing when the null hypothesis is not true and the sample size is small, often used in t-tests.

Poisson Binomial Distribution

A discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials, each with a different probability of success.

Power Distribution

A continuous probability distribution that models random variables that are positive-valued and have a heavy tail, often used to model extreme events or rare occurrences.

Rayleigh Distribution

A continuous probability distribution that models random variables that are positive-valued and have a skewed shape, often used to model wind speeds or wave heights.

Rice Distribution

A continuous probability distribution that models random variables that are positive-valued and have a skewed shape, often used to model the amplitude of a signal in communication systems.

Skellam Distribution

A discrete probability distribution that models the difference between two independent Poisson random variables, often used in the analysis of count data.

Slash Distribution

A continuous probability distribution that models random variables that are positive-valued and have a heavy tail, often used to model the size of earthquakes or the severity of insurance claims.

Stable Distribution

A continuous probability distribution that models random variables that are heavy-tailed and have stable shape, often used in financial modeling or time series analysis.

Truncated Normal Distribution

A continuous probability distribution that models random variables that are normally distributed but are constrained to a specified range, often used in decision analysis or risk assessment.

Tukey Lambda Distribution

A continuous probability distribution that models random variables that are symmetric and have heavy tails, often used in robust statistics or outlier detection.

Wald Distribution

A continuous probability distribution that models random variables that are positive-valued and have a skewed shape, often used in the analysis of survival data or reliability engineering.

Wigner Semi-Circle Distribution

A continuous probability distribution that models random variables that are symmetric and have a semi-circular shape, often used in quantum mechanics or random matrix theory.

Zero-Truncated Poisson Distribution

A discrete probability distribution that models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence, excluding the possibility of zero events.