Probability & Statistics Drills

Probability you can do under time

MA202 teaches each of these once, against one example, and moves on. This is the volume — thirty-three procedures from counting a sample space to updating a Beta prior, on questions generated fresh that never run out. Each stays green only while your recent answers hold.

Start this project See the modules

Modules: 9
Drills: 33
Build steps: 0
Time: ~8h

Walk out able to

Invert a conditional without losing the base rate, standardise any normal, and say what a p-value is not — without rebuilding the method first.

What you drill

Spaces, counts, conditionals

Axioms, sampling schemes, and Bayes on counts.

Distributions and moments

Discrete, continuous, and the spread of a sum.

Limits, error bars, bounds

What averages do, and what holds knowing almost nothing.

Estimates, tests, regression

Intervals, p-values, least squares, posteriors.

What you get

Skills that stick

Every project mixes short lessons, focused drills and real build steps, so you finish with working code and the judgement behind it.

You will practise

Sample spaces, conditioning, Bayes on counts
Discrete and continuous models, and moments
Limit theorems, standard errors, tail bounds
Estimation, hypothesis tests, regression

Afterwards you can

Invert a conditional and keep the base rate
Name a discrete model from the scene
Standardise a value and read the tail
Say what a p-value is, and what it is not

Modules

Step by step

Each module builds on the last. Read a short lesson, drill it until it's second nature, then put it to work.

1
The rules the subject obeys
~1h
Count a space, reduce it, and tell independence from disjointness.
- LessonWhat this project is for4 min
- DrillWork a consequence of the axioms12 min
- DrillCount the sample space16 min
- DrillRestrict, then renormalise16 min
- DrillIndependent, or just disjoint?16 min
2
Reverse the conditional
~1h
Go from effect back to cause without dropping the base rate.
- DrillSplit into cases, then recombine16 min
- DrillInvert the conditional16 min
- DrillWeigh the base rate20 min
- DrillMultiply the odds14 min
3
The named discrete models
~42 min
Read a mass function, name the model from the scene, and state its moments.
- DrillRead a mass function12 min
- DrillName the model from the scene14 min
- DrillState a model’s mean and variance16 min
4
Density, not probability
~52 min
Work a continuous model from its CDF, and standardise anything normal.
- DrillA density is not a probability14 min
- DrillUniform and exponential values12 min
- DrillStandardise it12 min
- DrillTransform a variable14 min
5
Mean, spread, moving together
~1h
Average and combine two variables without assuming independence you lack.
- DrillAdd and scale expectations14 min
- DrillCompute a variance12 min
- DrillCovariance and correlation14 min
- DrillCondition, then average14 min
- DrillRead a joint table20 min
6
What averages do
~40 min
Say which theorem applies, size the error, and bound a tail from little.
- DrillWhich limit theorem applies?14 min
- DrillSize the standard error12 min
- DrillBound a tail from almost nothing14 min
7
From sample to parameter
~42 min
Judge an estimator, fit one by likelihood, and attach an honest interval.
- DrillJudge an estimator14 min
- DrillMaximise the likelihood14 min
- DrillBuild a confidence interval14 min
8
Testing, and its limits
~1h
State a test, read its p-value correctly, and correct for multiplicity.
- LessonWhat this project cannot mark7 min
- DrillSet the test up14 min
- DrillRead a p-value14 min
- DrillName the error14 min
- DrillCorrect for multiplicity14 min
9
Lines and posteriors
~46 min
Fit a line, read a coefficient, and update a prior on evidence.
- DrillFit a least-squares line16 min
- DrillRead a regression coefficient14 min
- DrillUpdate a posterior16 min