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Practise probability
Answer one question at a time and review mistakes as you go.
Beta · Modules 1–5 · R practice aligned to Labs 2–9
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- 355
- Concepts
- 112
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Modules 1–5. Choose a published topic and start at your level.
M1.1
Introduction to Probability
Modelling uncertainty
0/12
M1.2
Sample Space and Events
Outcome design and event logic
0/24
M1.3
Probability Models
Axioms, counting, and models
0/28
M1.4
Conditional Probability
Updating with information
0/12
M1.5
Independent Events
Dependence and reliability
0/12
M1.6
Total Probability and Bayes
Prediction and reverse conditioning
0/8
M2.1
Discrete Random Variables
Numerical models of outcomes
0/11
M2.2
Mathematical Expectation
Probability-weighted averages
0/3
M2.3
Moments and Variability
Location and spread
0/4
M2.4
Bernoulli and Binomial Models
Repeated binary trials
0/8
M2.5
MGFs and Waiting-Time Distributions
Moments and waiting times
0/8
M2.6
Poisson Models
Event counts and rare-event approximation
0/6
M3.1
Densities, distribution functions and empirical distributions
Move from histogram area to probability, distinguish density from mass, and interpret distribution functions.
0/12
M3.2
Continuous moments, generating functions and quantiles
Compute weighted integrals and quantiles while checking existence and the domain of an mgf.
0/12
M3.3
Uniform and exponential models
Use interval lengths, waiting-time rates and the memoryless property with consistent units.
0/9
M3.4
Gamma and chi-square distributions
Connect the gamma function, shape and scale, Poisson arrival times and chi-square models.
0/12
M3.5
Distributions under transformation
Map support, invert monotone transformations, include every branch and distinguish continuous from discrete rules.
0/21
M4.1
Joint laws, marginals and trinomial counts
Read and integrate joint laws, check independence on the full support and compute functions of pairs.
0/15
M4.2
Covariance, correlation and conditioning
Separate linear association from independence and use conditional laws, total mean and total variance.
0/24
M4.3
Transformations of pairs
Use inverse Jacobians and transformed supports; identify gamma-beta and F constructions.
0/12
M4.4
Independent samples, sums and probability bounds
Study statistics before observation, product mgfs, sums, Chebyshev bounds and convergence in probability.
0/18
M5.1
Normal Distribution Foundations
Read normal parameters, standardise probabilities, invert symmetric intervals, and identify the normal MGF.
0/12
M5.2
Functions of Normal Samples
Distinguish exact normal, chi-square, and Student t results and the independence assumptions behind them.
0/30
M5.3
Central Limit Theorem
Apply the CLT to means and sums, judge approximation assumptions, and understand the taught MGF argument.
0/9
M5.4
Normal Approximations to Counts
Approximate binomial, Poisson and trial-count negative-binomial probabilities with the correct scale and continuity correction.
0/12
M5.5
Limiting MGFs
Identify limiting laws, distinguish rare-event and fixed-probability limits, and interpret a degenerate limit.
0/9
M5.6
Bivariate Normal Distribution
Separate joint normality from normal marginals and calculate conditional normal parameters and independence.
0/12