core practice · coding problem
Match distribution to scenario
For each scenario, name the best distribution: (1) 10,000 coin flips, count heads. (2) Rare server crashes, ~2 per day. (3) Time until next request in a Poisson stream. (4) Average of 500 independent user latencies.
The mechanism
Distributions are reusable uncertainty templates. Bernoulli/Binomial for yes/no counts; Poisson for rare events in fixed windows; Normal for sums of many small pieces (CLT); Exponential for waiting times between events.
Expected evidence
(1) Binomial (≈Normal for large n). (2) Poisson. (3) Exponential. (4) Normal for the sample mean (CLT).
Try this drill in the practice workspace →
Hints when you need them
- Counts with fixed trials → Binomial.
- Waiting times → Exponential; rare counts in window → Poisson.
Watch for these mistakes
- Using a Normal model on tiny counts or heavy tails
- Confusing Poisson rate λ with probability
- Applying Binomial when trials are not independent