"In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment."
Various types of probability distributions like binomial, normal, Poisson, etc.
Basic Probability Concepts: This covers the basics of probability such as sample space, events, and probability axioms.
Random Variables and Probability Distributions: This entails the definition of random variables, probability functions, their types, and their properties.
Discrete Probability Distribution Functions: This involves the understanding of probability functions for discrete events like binomial, Poisson, geometric, and hypergeometric.
Continuous Probability Distribution Functions: This covers probability functions for continuous events like normal distributions, exponential distributions, and gamma distributions.
Joint Probability Distributions: This covers the definition and types of joint distributions, conditional probability, and covariance.
Moment Generating Functions: These are functions used to derive the moments of probability distributions.
Central Limit Theorem: This theorem is used to describe the behavior of sample means in large samples.
Hypothesis Testing: These are procedures that allow us to make inferences about a population from a sample.
Estimation: This covers the methods of estimating population parameters from a sample.
Markov Chains: This is usually covered under stochastic modeling, and it involves analyzing how the likelihood of a future event depends solely on the present state.
Bayesian Statistics: This involves updating probabilities based on prior probabilities and new evidence.
Simulation: This involves using statistical software to generate data used to obtain probability distributions.
Expected Value and Variance: This covers the definitions of expected value and variance of a probability distribution.
Percentiles: These are used to describe the position of an observation in a distribution.
Normal Distribution: A bell-shaped curve that represents a continuous probability distribution.
Binomial Distribution: A discrete probability distribution that shows the probability of the number of successes in a fixed number of trials.
Poisson Distribution: A discrete probability distribution that shows the probability of the number of events occurring in a fixed time or space.
Exponential Distribution: A continuous probability distribution that shows the probability of the time between consecutive events following an exponential distribution.
Weibull Distribution: A continuous probability distribution that is used in reliability analysis to model the time of failure of a system.
Gamma Distribution: A continuous probability distribution that is used to model the time to take a certain number of events to occur.
Beta Distribution: A continuous probability distribution that models the probability of a random variable taking a value between 0 and 1.
Chi-Squared Distribution: A continuous probability distribution that is used in hypothesis testing and statistical inference.
Uniform Distribution: A continuous probability distribution that models random events that are equally likely to happen.
Logistic Distribution: A continuous probability distribution that is used to model the probability of an event in response to a stimulus over time.
"Probability distributions can be defined in different ways and for discrete or continuous variables."
"It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space)."
"More commonly, probability distributions are used to compare the relative occurrence of many different random values."
"For instance, if X is used to denote the outcome of a coin toss ('the experiment'), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair)."
"Probability distributions are used to compare the relative occurrence of many different random values."
"Distributions with special properties or for especially important applications are given specific names."
"Distributions with special properties or for especially important applications are given specific names."
"Distributions can be defined...for discrete or continuous variables."
"...the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment."
"It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space)."
"...the probability distribution of X would take the value 0.5 for X = tails (assuming that the coin is fair)."
"assuming that the coin is fair."
"...probability distributions are used to compare the relative occurrence of many different random values."
"...the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment."
"Distributions with special properties or for especially important applications are given specific names."
"if X is used to denote the outcome of a coin toss ('the experiment')"
"In probability theory and statistics, a probability distribution is the mathematical function..."
"Probability distributions are used to compare the relative occurrence of many different random values."
"...the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment."