Probability Glossary
25 essential terms — because precise language is the foundation of clear thinking in Probability.
Showing 25 of 25 terms
A formula that relates conditional probabilities: $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$, used to update beliefs with new evidence.
A discrete probability distribution describing the number of successes in $n$ independent Bernoulli trials with success probability $p$.
A theorem stating that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population distribution.
An unordered selection of $r$ items from $n$ distinct items: $\binom{n}{r} = \frac{n!}{r!(n-r)!}$.
The probability of an event $A$ given that event $B$ has occurred, calculated as $P(A|B) = \frac{P(A \cap B)}{P(B)}$.
$F(x) = P(X \leq x)$, a function that gives the probability that a random variable takes a value less than or equal to $x$.
A subset of the sample space representing one or more outcomes of interest.
The weighted average of all possible values of a random variable, where weights are the probabilities of each value.
Two events are independent when the occurrence of one does not affect the probability of the other: $P(A \cap B) = P(A)P(B)$.
The probability that two or more events occur simultaneously: $P(A \cap B)$.
A theorem stating that the sample mean converges to the expected value as the number of trials approaches infinity.
The probability of a single event without reference to other events, obtained by summing or integrating the joint probability over all values of the other variables.
Two events are mutually exclusive if they cannot both occur simultaneously, meaning $P(A \cap B) = 0$.
A continuous probability distribution with a symmetric bell-shaped curve, defined by mean $\mu$ and standard deviation $\sigma$.
An ordered arrangement of $r$ items selected from $n$ distinct items: $P(n,r) = \frac{n!}{(n-r)!}$.
A discrete distribution that models the number of events occurring in a fixed interval at a constant average rate $\lambda$.
The updated probability of a hypothesis after incorporating new evidence via Bayes' theorem.
The initial probability of a hypothesis before observing new evidence, used as input in Bayesian analysis.
A numerical measure between 0 and 1 that quantifies the likelihood of an event occurring.
A function $f(x)$ that describes the relative likelihood of a continuous random variable taking a value near $x$; the area under the curve over an interval gives the probability.
A function that assigns a numerical value to each outcome in a sample space.
The set of all possible outcomes of a random experiment, typically denoted by $S$ or $\Omega$.
The square root of the variance, providing a measure of spread in the same units as the random variable.
A measure of how spread out the values of a random variable are around the mean, equal to $E[(X - \mu)^2]$.
The number of standard deviations a value is from the mean: $z = \frac{x - \mu}{\sigma}$. Used to standardize values from any normal distribution to the standard normal distribution.