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Discrete Random Variables and Probability Models
Map uncertain business outcomes to a countable numerical variable with a clearly defined support.
38 min3 outcomes
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Module 6
Model counts, arrivals, successes, finite-population samples, waiting times, and business risk using discrete probability distributions.
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Distribution Modeler
Lessons
18
Status
Available
Progress
0%
Map uncertain business outcomes to a countable numerical variable with a clearly defined support.
Construct a custom PMF and verify unique support, nonnegative mass, and total probability one.
Use PMF and CDF views to answer exact, cumulative, interval, and tail questions.
Calculate a probability-weighted long-run average and use it in expected profit or cost decisions.
Measure probability-weighted dispersion and interpret standard deviation in the original units.
Model equally likely consecutive integers and compare theoretical with simulated frequencies.
Represent one binary trial with a clearly named success event and probability p.
Diagnose the fixed-n, binary, constant-p, independence, and success-count assumptions.
Calculate point probabilities and connect n and p to center, spread, and skew.
Translate verbal probability statements into precise inclusive integer boundaries.
Evaluate whether a stable-rate event-count model is reasonable for a fixed exposure.
Calculate Poisson point and tail probabilities while matching lambda to the requested exposure.
Compare exact binomial probabilities with a labelled Poisson approximation using lambda=np.
Calculate exact success counts when sampling without replacement from a finite population.
Evaluate a binomial approximation using p=K/N and a visible sampling fraction.
Model trials until the first success while translating the course convention to base R.
Transform costs and combine uncertain quantities using covariance-aware mean and variance rules.
Integrate custom, binomial, Poisson, hypergeometric, geometric, and covariance models in an auditable operating decision.
Distribution modelling library
All values, scenarios, worksheets, and scripts are original to STATLAB Academy. The prerequisite Module 5 probability foundation is recommended.