Expected Value of a Discrete Distribution Calculator
Calculates the expected value E[X] = Σ xᵢ·P(xᵢ) and variance Var[X] = Σ(xᵢ−μ)²·P(xᵢ) for a discrete probability distribu...
Calculators and explainers tagged under Probability.
Calculates the expected value E[X] = Σ xᵢ·P(xᵢ) and variance Var[X] = Σ(xᵢ−μ)²·P(xᵢ) for a discrete probability distribu...
Calculates the binomial probability mass function P(X = k) and cumulative distribution P(X ≤ k) from trials n, success p...
Calculates the mean and variance of a negative binomial distribution from the number of required successes r and success...
Compute the probability of rolling exactly, at least, or at most a chosen sum on N fair dice with S sides each.
Calculates the probability of exactly r failures before the k-th success in independent Bernoulli trials using the negat...
Applies Bayes' theorem to update a prior probability with new evidence, outputting the posterior probability and likelih...
Generate one or more random integers in a chosen range, with optional uniqueness and optional sorting.
Calculates probability mass, mean μ = (a+b)/2, variance σ² = (n²−1)/12, and P(X ≤ k) for a discrete uniform distribution...
Compute the Poisson probability of observing exactly k events when the average rate is λ events per interval.
Calculates the exact binomial probability P(X = k) = C(n,k) · pᵏ · (1−p)^(n−k), the mean μ = n·p, and standard deviation...
Calculates the Poisson PMF and CDF from event rate λ and number of events k for modelling rare events in a fixed time/sp...
Calculates the probability of achieving the first success on exactly the k-th trial in a geometric distribution, plus me...
Count how many ways to choose or arrange r items from a set of n — both nPr and nCr, with a short breakdown of why they...
Given a discrete random variable with three outcomes x₁, x₂, x₃ and corresponding probabilities p₁, p₂, p₃ (summing to 1...
Convert betting odds expressed as "X to Y for the event" into the implied probability of the event occurring, with the c...
Compute the binomial probability of getting exactly k successes in n independent trials, each with probability of succes...
Compute the conditional probability P(A | B) from the joint probability P(A ∩ B) and the marginal P(B). Reports P(B | A)...
Calculates the mean and variance of a geometric distribution modelling the number of trials until the first success.
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