Probability distributions: Normal N(μ,σ²) — bell curve, Binomial B(n,p) — n trials, Poisson P(λ) — rare events, Exponential Exp(λ) — wait times. PDF gives probability density; CDF gives P(X≤x). Mean = E[X], Variance = E[(X−μ)²].
How to Use
Select a distribution:
- Parameters: μ, σ, n, p, λ
- Evaluate: P(X=x), P(X≤x)
- Output: PDF/CDF + statistics
Distributions
- Normal: continuous, symmetric bell
- Binomial: discrete, n trials with p
- Poisson: discrete, rate λ events
- Exponential: continuous, memoryless
Which Distribution?
Fixed trials → Binomial. Count per interval → Poisson. Time between events → Exponential. Sum of many variables → Normal (CLT).
Step-by-Step Instructions
- 1Select distribution type.
- 2Enter parameters.
- 3Enter x value.
- 4View PDF and CDF.
- 5Check mean and variance.