⁝Probability & Statistics
Probability, statistics, stochastic processes, Bayesian statistics
Subfields
Probability
Basic probability, conditional, distributions, expected value, variance
Statistics
Descriptive, inferential statistics, hypothesis testing, regression
Stochastic Processes
Markov chains, Brownian motion, Poisson processes
Bayesian Statistics
Bayes theorem, prior/posterior probability, MCMC
Queueing Theory
Queue models, network traffic, service systems
Information Theory
Entropy, mutual information, channel capacity, data compression
Concepts
Probability Basics
Probability is a number between 0 and 1 representing the likelihood of an event occurring. 0 means impossible, 1 means certain.
Conditional Probability
Conditional probability P(A|B) is the probability of event A occurring given that event B has occurred.
Expected Value
Expected value (mean) is the probability-weighted average of all possible values. It represents the long-run average.
Variance and Standard Deviation
Variance measures how spread out data is from the mean. Standard deviation is the square root of variance.
Normal Distribution
The normal (Gaussian) distribution is a continuous probability distribution with a bell-shaped curve symmetric around the mean. It appears widely in nature and society.
Binomial Distribution
The binomial distribution models the number of successes in n independent trials, each with success probability p.
Central Limit Theorem
The Central Limit Theorem states that with sufficient sample size, the distribution of sample means approaches a normal distribution regardless of the original distribution.
Poisson Distribution
A distribution modeling the number of rare events occurring in a fixed interval of time or space.
Independent Events
Two events are independent if the occurrence of one doesn't affect the probability of the other.
Bayes' Theorem
A theorem for updating prior probability with new evidence to compute posterior probability.
Hypothesis Testing
A statistical method to test claims about a population using sample data.
Correlation
Measures the strength and direction of a linear relationship between two variables. Ranges from -1 to 1.
Regression Analysis
A statistical method to model and predict the relationship between dependent and independent variables.