Probability Distributions Explained
Distributions describe uncertainty. Learn common families, visualize shapes, and connect parameters to moments.
📚 Common Distributions
- Normal(μ, σ²): bell curve, CLT limit
- Binomial(n, p): number of successes in n trials
- Poisson(λ): counts in a fixed interval
- Exponential(λ): waiting times, memoryless
❓ Frequently Asked Questions
1) PDF vs PMF?
PDF integrates to probabilities; PMF sums to probabilities.
PDF integrates to probabilities; PMF sums to probabilities.
2) Why normal is ubiquitous?
Central Limit Theorem makes sums tend normal.
Central Limit Theorem makes sums tend normal.
3) Parameter estimation?
Method of moments, maximum likelihood, Bayesian updating.
Method of moments, maximum likelihood, Bayesian updating.
4) Heavy tails?
Power laws and t-distributions have higher tail probability.
Power laws and t-distributions have higher tail probability.
5) CDF usage?
Compute tail probabilities and quantiles.
Compute tail probabilities and quantiles.