Probability Distribution Calculator
Calculate and visualize probability distributions including normal, Poisson, and binomial distributions.
Distribution Parameters
Distribution Type
Mean (μ)
Average value of the distribution
Standard Deviation (σ)
Measure of spread
How to Use
Step-by-Step Guide
- 1.Select your probability distribution type
- 2.Enter the required parameters for your chosen distribution
- 3.Click "Calculate Distribution" to analyze and visualize
- 4.Review the probability mass function and cumulative distribution
- 5.Use the visualization to understand the distribution shape
Distribution Types
- Normal Distribution: Bell-shaped curve, used for natural phenomena, heights, measurement errors
- Poisson Distribution: Discrete events, used for call centers, traffic analysis, rare events
- Binomial Distribution: Fixed trials with two outcomes, used for quality control, medical trials
Distribution Formulas
Normal Distribution
f(x) = (1/σ√2π) e^(-½(x-μ)²)
Probability density function
Poisson Distribution
P(X=k) = (λ^k e^(-λ)) / k!
Probability of exactly k events
Binomial Distribution
P(X=k) = C(n,k) p^k (1-p)^(n-k)
Probability of k successes in n trials
Common Applications
Statistics & Research
Hypothesis testing, quality control, and modeling natural phenomena with statistical distributions.
Finance & Risk
Insurance claims modeling, investment risk assessment, and financial option pricing.
Engineering & Science
Reliability analysis, queue modeling, and experimental design with probabilistic outcomes.
Frequently Asked Questions
What is a probability distribution?
A probability distribution describes the likelihood of different outcomes in a random experiment. It shows how probabilities are distributed across possible values.
When should I use normal vs Poisson distribution?
Use normal distribution for continuous data (heights, measurements). Use Poisson for discrete count data (customer arrivals, defects).
What does the area under the curve represent?
For continuous distributions, the area under the curve between two points represents the probability of the random variable falling within that range.
How do I choose the right distribution?
Consider your data type (continuous vs discrete), the nature of the process, and whether events are independent trials or counts over time.
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Key Takeaways
Statistical Modeling
Probability distributions provide mathematical models for understanding random phenomena and making data-driven predictions.
Decision Support
Understanding probability distributions helps quantify uncertainty and make more informed decisions under risk.
Scientific Analysis
Proper distribution selection and parameter estimation is fundamental to accurate statistical inference and research.
Risk Assessment
Probability distributions enable precise risk calculation and scenario analysis across finance, engineering, and science.