Overview

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BiteSize Statistics for Absolute Beginners: Key Probability Distributions is the third and final course in the BiteSize Stats for Absolute Beginners specialization. It shows how the probability rules from Course 2 turn into named, reusable models — random variables and their distributions, the binomial and Poisson families for discrete counts, the Normal distribution for continuous measurements, and the sampling distributions that connect any of them back to real data. Across five modules, learners progress from random variables, PMFs, expected value, and CDFs, through the binomial distribution for fixed-trial counts and the Poisson distribution for rate-based counts, to the Normal distribution, Z-scores, and inverse-Normal problems, and finally the Central Limit Theorem and sampling distributions of the mean and proportion. Every core lesson pairs a short video walkthrough and reading with a hands-on interactive notebook built around a realistic business scenario, and each module closes with a graded applied lab using a real dataset; two modules also include a fully worked bonus case study.

Syllabus

Random Variables and Their Distributions

Introduces the random variable as the bridge between random experiments and numerical analysis, distinguishing discrete from continuous types. Students define and verify probability mass functions, calculate expected value and variance to summarize a distribution's center and spread, and use the cumulative distribution function to answer threshold probability questions.

The Binomial Distribution

Covers the four BINS conditions that define a binomial setting, the binomial probability formula, and how the distribution's shape, mean, and standard deviation depend on n and p. Students apply exact binomial probabilities to defect-rate monitoring, conversion-rate analysis, and acceptance sampling.

The Poisson Distribution

Covers the conditions that define a Poisson setting, the Poisson probability formula, and the distinctive property that its mean and variance are both equal to lambda. Students rescale rates across time/space intervals and apply Poisson probabilities to call-center staffing, insurance claims, and server capacity, closing with a fully worked queueing-theory case study.

The Normal Distribution

Introduces the Normal distribution's bell-curve shape and its two governing parameters, the 68-95-99.7 empirical rule, and Z-score standardization for comparing values across scales. Students compute forward Normal probabilities and inverse Normal percentiles, applying both to quality control, pricing, and Value-at-Risk problems.

Sampling Distributions and the Central Limit Theorem

Covers the sampling distribution of the sample mean and the standard error, then the Central Limit Theorem — why the sample mean is approximately Normal for large n regardless of the population's shape. Students apply CLT-based probability calculations to sample means and sample proportions, closing with a lab that simulates the theorem empirically.