Probability Distributions Visualizer
Explore binomial, Poisson, geometric, and uniform distributions. Adjust parameters and see the probability mass function, mean, and variance update instantly.
Distribution Parameters
Properties
| Distribution | -- |
| PMF | -- |
| Parameters | -- |
| Mean | -- |
| Variance | -- |
| Std Dev | -- |
The Math Behind It
Discrete Distributions
- Binomial: P(X=k) = C(n,k) pk(1-p)n-k — n trials, probability p of success
- Geometric: P(X=k) = (1-p)k-1 p — trials until first success
- Uniform: P(X=k) = 1/n — equal probability for all outcomes
- Each distribution has a probability mass function (PMF) that sums to 1
- Mean and variance characterize the center and spread
Poisson Distribution
- Models the count of rare events in a fixed interval
- P(X=k) = λk e-λ / k!
- λ is the expected rate (average count)
- Key property: mean = variance = λ
- For large λ, the Poisson approaches a normal distribution
- Used for traffic arrivals, radioactive decay, server requests
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