Probability Distribution Calculator

Calculate PMF/PDF, CDF, mean and variance for common discrete and continuous distributions.

Inputs

Distribution

n (trials, for Binomial)

p (probability, for Binomial/Geometric)

λ (rate, for Poisson)

μ (mean, for Normal)

σ (std dev, for Normal)

x (value to evaluate)

PMF/PDF at x

0.26682793

CDF at x: P(X ≤ x)

0.64961072

Distribution Mean

3.000000

Distribution Variance

2.100000

Step by step

Values used
Distribution = Binomial; n (trials, for Binomial) = 10; p (probability, for Binomial/Geometric) = 0.3000; λ (rate, for Poisson) = 4; μ (mean, for Normal) = 0; σ (std dev, for Normal) = 1; x (value to evaluate) = 3
Binomial PMF
P(X=k) = C(n,k) × p^k × (1−p)^(n−k)
Normal PDF
f(x) = (1/(σ√(2π))) × exp(−(x−μ)²/(2σ²))
PMF/PDF at x
= 0.26682793
CDF at x: P(X ≤ x)
= 0.64961072
Distribution Mean
= 3.000000
Distribution Variance
= 2.100000

How it works

This multi-distribution calculator evaluates PMF (for discrete) or PDF (for continuous), along with the CDF, mean and variance. Select a distribution and provide its parameters to evaluate at any point x.

Formulas

Binomial PMF

P(X=k) = C(n,k) × p^k × (1−p)^(n−k)

n: Trials
k: Successes
p: Success probability

Normal PDF

f(x) = (1/(σ√(2π))) × exp(−(x−μ)²/(2σ²))

μ: Mean
σ: Standard deviation

Frequently Asked Questions

What is the difference between PMF and PDF?

PMF (probability mass function) is for discrete distributions — it gives the exact probability of a specific value. PDF (probability density function) is for continuous distributions — it gives density, not probability, at a point.

What is the CDF?

The cumulative distribution function CDF(x) = P(X ≤ x), the probability of observing a value at most x.

You might also need

Normal Distribution Calculator Binomial Distribution Calculator Poisson Distribution Calculator