Probability Distributions

Probability calculators and formulas for Bayes' theorem and standard distributions. Includes normal distribution, binomial distribution, and conditional probability calculations.

14Formulas

All levels Difficulty

Updated Oct 2026

← All Statistics & Probability (32) Probability Distributions (14)

Fundamental

One-Sample t-Statistic

t = (x̄ - μ0) / (s/√n)

Fundamental

Chi-Square Test Statistic

χ² = Σ((O - E)² / E)

Fundamental

Standard Error of the Mean

SE = σ / √n

Fundamental

Margin of Error

ME = z * (σ/√n)

Fundamental

Confidence Interval for the Mean

CI = x̄ ± z*(σ/√n)

Fundamental

Conditional Probability

P(A|B) = P(A∩B) / P(B)

Fundamental

Variance of a Discrete Random Variable

Var(X) = E(X²) - [E(X)]²

Fundamental

Expected Value (Discrete Random Variable)

E(X) = Σ(xᵢ * P(xᵢ))

Fundamental

Normal Distribution Probability Density

f(x) = (1/(σ√(2π))) * e^(-(x-μ)²/(2σ²))

Fundamental

Poisson Probability

P(X=k) = (λ^k * e^-λ) / k!

Fundamental

Combinations

nCr = n! / (r! * (n - r)!)

Fundamental

Permutations

nPr = n! / (n - r)!

Fundamental

Binomial Probability

P(X=k) = C(n,k)pᵏ(1−p)ⁿ⁻ᵏ

Fundamental

Bayes' Theorem

P(A|B) = P(B|A)P(A) / P(B)