Distributions

Normal, Binomial, and Poisson distributions.

Not started3 min explanation

Visualize, practice, and deep-dive material are optional—use only what helps you learn.

Explanation

A focused 3-minute explanation using the topic's authored material.

Learning goals and prerequisites

After this lesson

Select defensible distributions for observed data
Estimate parameters and quantify uncertainty
Recognize misspecification, heavy tails, and mixtures

Helpful before starting

Probability fundamentals
Differentiation and integration
Expectation, variance, and covariance

Start here

Distributions, in plain language

Normal, Binomial, and Poisson distributions. Distributions connect data-generating assumptions to estimators, likelihoods, simulations, confidence intervals, and generative models.

For a small example, two sets share mean 5 but have very different variability. Plot both, calculate variance, and notice why one number cannot describe shape. This is the mechanism to keep in view as the lesson becomes more technical. Before moving on, identify the input, transformation, output, and one observation that would falsify your conclusion.

Key points

PMFs, PDFs, CDFs, quantiles, moments, and support.
Bernoulli, binomial, categorical, Poisson, uniform, Gaussian, and exponential families.
Sampling distributions, law of large numbers, and central limit theorem.

Use it well

When Distributions helps—and where it breaks

Most requests are fast but a few are extremely slow. Use quantiles and a right-skewed model instead of relying on average latency, then investigate the tail. A useful result still depends on checking the assumptions and evidence below rather than treating one successful output as proof.

Key points

Assuming normality by default. Better approach: Inspect skew, tails, bounds, and generation mechanisms first.
Selecting by likelihood alone. Better approach: Combine fit statistics with residual checks and domain validity.
Using the CLT as a small-sample guarantee. Better approach: Check dependence, variance, and convergence empirically.

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