1.13 Random variables and distributions
You can pick the right distribution for a modelling assumption.
Before:00. Orientation & SetupUnlocks:03. Data Handling & Analysis04. Classical AI — Agents, Search & Knowledge Representation
Distributions are the vocabulary of modelling assumptions: choosing binomial against Poisson against normal is choosing what you believe about the data. PMF, PDF and CDF are three views of one object, and moving between them freely is the fluency this topic builds. It follows Bayes because updating beliefs requires named distributions to update. The trap is reading a density value as a probability — for continuous variables only areas mean anything, and densities can happily exceed one.
Work through these
Discrete: Bernoulli, binomial, Poisson, categorical
The standard distributions for counts and categories, each corresponding to a different kind of experiment. Choosing the right one is a modelling decision, not a formula lookup.
Continuous: uniform, normal, exponential, beta, gamma
The standard continuous distributions, and what shape of quantity each is a natural description for. Recognising the shape of your data narrows the choice quickly.
PMF, PDF, CDF, quantiles
The mass function, the density, the cumulative version and the quantiles are four views of the same distribution. Knowing which one a question needs saves a lot of confusion.
Transformations of random variables
What happens to a distribution when you apply a function to the variable, which is how new distributions arise from old ones. It also explains why some transformations of data are conventional.
Sign in to keep your progress.
Free resources
We haven't checked most of these for screen reader use yet.
Links last checked 29 Aug 2026.
Stuck here?
Ask a mentor. A real person answers, and they can see exactly which topic you're on. Usually within a couple of working days.
Checking your session…
Topics shown in module order.