9 parts · 9 chapters
Probability and Statistics for Engineers
The statistics engineers actually need: reading latency, running experiments, sizing systems and trusting benchmarks. Every number in the course comes from a seeded simulation you can rerun. Peeking at an A/A test 20 times turned a 5% false-positive rate into 24.1%, and a p99 estimated from 2,000 samples had a 95% interval from 96 to 697 ms.
Nine parts: distributions; percentiles and tails; sampling; confidence intervals with the bootstrap; A/B testing and its traps; regression; Bayesian thinking (a 99%-sensitive fraud flag was right only 19.9% of the time at a 0.5% base rate); queueing theory and Little's law; and benchmark statistics.
shapeLatency is skewed: means mislead, percentiles inform.
tailsFan-out turns rare slowness into common slowness.
uncertaintyEvery estimate needs an interval.
experimentsSample size first, no peeking, one metric decided in advance.
beliefsBase rates dominate rare-event detection.
capacityQueues explode as utilisation approaches 100%.
00
Distributions
Simulate to understand
1 ch · ~8 min01Percentiles and Tails
Percentiles, and why tails multiply
1 ch · ~8 min02Sampling
Samples from streams
1 ch · ~8 min03Confidence Intervals
Intervals for anything with the bootstrap
1 ch · ~8 min04A/B Testing and Its Traps
Simulated: what peeking does
1 ch · ~8 min05Regression
Fit, check, do not over-read
1 ch · ~8 min06Bayesian Thinking
Base rates decide everything
1 ch · ~8 min07Queueing Theory and Little's Law
Queues explode near 100%
1 ch · ~8 min08Benchmark Statistics
Is it really faster?
1 ch · ~8 minFor programmers without a CS degreeUses Discrete Maths for counting; feeds SRE, Systems Performance, Product Engineering experiments and the ML maths course.