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Beginnerprobabilitydistributionsbayesmarkov-chains

Probability Foundations

31 problems·~10h·4 stages

The language of uncertainty, from counting and expectation to Markov chains and concentration bounds. You will implement Bayes rule, classic distributions, inclusion-exclusion, gambler's ruin, and a CLT simulation. A good fit for interviews and for anyone starting probabilistic ML.

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What you will learn

  • Count outcomes with permutations, combinations, and inclusion-exclusion
  • Work with geometric, binomial, Poisson, exponential, and normal distributions
  • Apply conditional probability, total probability, and Bayes' rule
  • Analyze Markov chains, hitting times, and limit theorems

1Counting and Basics

0/8

Probability starts with counting. Combinations, permutations, factorials, complements, independence, and the expectation of indicator variables.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepCredit Default DetectorMedium

2Random Variables and Distributions

0/8

Expected value and variance, then the distributions that recur: geometric, Poisson, exponential, and normal, plus covariance between indicators.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepCredit Default DetectorMedium

3Conditional Probability and Bayes

0/7

Update beliefs with evidence: conditional tables, total probability, Bayes with two and three hypotheses, multinomial counts, hypergeometric sampling, and CDFs.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepCredit Default DetectorMedium

4Chains and Limit Theorems

0/8

Sequences of random events: stationary distributions, inclusion-exclusion, Markov n-step laws, hitting times, gambler's ruin, the Central Limit Theorem, and a Chernoff bound.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepCredit Default DetectorMedium

Capstone

Collection

Close the path with one real artifact from the catalog.

Probability & Statistics Core

Blend the counting, distribution, and Bayes work in this path with one compact mixed set.