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...
Compute the posterior probability P(A|B) from the prior P(A), the likelihood P(B|A), and the false-positive rate P(B|¬A)...
Calculates Poisson probabilities: P(X=k) = e^(−λ)·λᵏ/k!, and the cumulative P(X≤k) by summing from 0 to k. Used for coun...
Calculates the probability of achieving the first success on exactly the k-th trial in a geometric distribution, plus me...
Generate one or more random integers in a chosen range, with optional uniqueness and optional sorting.
Compute the binomial probability of getting exactly k successes in n independent trials, each with probability of succes...
Calculates the probability of exactly r failures before the k-th success in independent Bernoulli trials using the negat...
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...
Compute the Poisson probability of observing exactly k events when the average rate is λ events per interval.
Convert a raw value into a z-score using the mean and standard deviation of its distribution, and look up the correspond...
Given a discrete random variable with three outcomes x₁, x₂, x₃ and corresponding probabilities p₁, p₂, p₃ (summing to 1...
Calculates the hypergeometric probability of drawing exactly k successes from a finite population without replacement.
Calculates the binomial probability mass function P(X = k) and cumulative distribution P(X ≤ k) from trials n, success p...
Calculates the Poisson PMF and CDF from event rate λ and number of events k for modelling rare events in a fixed time/sp...
Compute the probability of exactly k heads (or any chosen number) in n independent fair-coin flips, using the binomial d...
Compute the probability that at least two people in a group share the same birthday, using the classic 1 − (365! / ((365...
Compute the probability of rolling exactly, at least, or at most a chosen sum on N fair dice with S sides each.
Calculates the exact binomial probability P(X = k) = C(n,k) · pᵏ · (1−p)^(n−k), the mean μ = n·p, and standard deviation...
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