Distribution Calculator - Probability & Statistics
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How It Works
Select Distribution
Choose normal, binomial, or Poisson
Enter Parameters
Input distribution parameters
Apply Formula
Use PDF/PMF equations
Common Examples
Distribution Calculator
What
A tool for calculating probability distributions including normal, binomial, and Poisson distributions.
Why
Essential for statistical analysis, probability theory, and data science applications.
Applications
Statistics, quality control, risk analysis, machine learning, and scientific research.
Calculation Examples
| Distribution | Parameters | P(X=2) | Application |
|---|---|---|---|
| Normal | μ=0, σ=1 | 0.0540 | Standard normal |
| Binomial | n=10, p=0.3 | 0.2335 | Quality control |
| Poisson | λ=3 | 0.2240 | Arrival rates |
| Normal | μ=100, σ=15 | 0.0000 | IQ scores |
Frequently Asked Questions
What is a probability distribution?
A probability distribution describes how probabilities are distributed over the values of a random variable. It shows the likelihood of different outcomes.
When should I use a normal distribution?
Use normal distribution for continuous data that clusters around a mean, like heights, weights, test scores, or measurement errors. It's the bell curve distribution.
What is a binomial distribution used for?
Binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success (like coin flips or pass/fail tests).
When do I use Poisson distribution?
Poisson distribution models the number of events occurring in a fixed interval (time/space) when events happen independently at a constant average rate.
What's the difference between PDF and PMF?
PDF (Probability Density Function) is for continuous distributions like normal. PMF (Probability Mass Function) is for discrete distributions like binomial and Poisson.
How accurate are these calculations?
The calculator uses precise mathematical formulas and provides results accurate to 6 decimal places. Results are suitable for academic and professional use.
Can I see the calculation steps?
Yes! The calculator shows detailed step-by-step solutions including the formulas used, parameter substitution, and final calculations for educational purposes.