Advanced~8h

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.

The pitch

What you practise, and what you leave with

No artifact. What you leave with is speed: the mechanical half of a statistics course, current rather than once-understood.

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

9 modules, 35 items

Lessons explain one idea. Drills repeat it until it sticks. Build steps make something that exists afterwards.

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