Foundational for decision-making under uncertainty.
Engineering Applications
- A/B Testing: Confidence intervals, p-values, sample size calculations
- Ranking Systems: Bayesian inference, prior/posterior updates
- Error Budgets: Expected value, variance, percentiles
- Retry Logic: Exponential backoff, jitter calculations
- Capacity Planning: Percentile estimation, tail distributions
Key Concepts
Expected Value
E[X] = Σ x_i * P(x_i)
Use for: Comparing strategies with uncertain outcomes
Variance & Standard Deviation
Var(X) = E[(X - μ)²]
σ = √Var(X)
Use for: Understanding spread of outcomes, risk assessment
Bayes’ Theorem
P(A|B) = P(B|A) * P(A) / P(B)
Use for: Updating beliefs with new evidence, ranking systems
Confidence Intervals
CI = x̄ ± z * (σ/√n)
Use for: A/B testing, sample size planning
Quick Reference: Distributions
| Distribution | Use Case |
|---|---|
| Normal | Central limit theorem, aggregates |
| Exponential | Time between events, retry timing |
| Poisson | Event counts per interval |
| Binomial | Success/failure counts |
| Beta | Probability of probability (ranking) |
System Design Connections
Retry with Jitter
delay = min(cap, base * 2^attempt) + random(0, jitter)
Prevents thundering herd, smooths load.
Percentile Latency
p50 tells you typical experience.
p99 tells you tail experience.
p99.9 tells you worst-case SLO risk.
Related
- Systems Thinking
- Persistence Framework – Decision-making under uncertainty
- Property-Based Testing – Statistical testing approaches
