Free module · Quantitative toolkit
Statistics & Probability
Every price move is signal plus randomness. Statistics is how you tell them apart.
entry · validation
The building blocks
- Count possible outcomes first.
- A probability measures how likely an event is.
- Separate outcomes, distributions and averages
- Measure sampling uncertainty and conditional probabilities
- Evaluate edge, calibration and tail assumptions
Lessons in this module
- Start with counts, probabilities and averages
- Random outcomes, sample averages and the limits of the bell curve
- Conditional probability: update a belief with evidence
- Prediction markets: probability, price and net expected value
- Expected value: measure the payoff before choosing the risk
- Correlation: how many strategies do you really have?
- Conditional probability and Bayes: where the edge actually lives
- The central limit theorem: sampling means under explicit assumptions
- Estimation uncertainty and Bayesian updating
Practice and apply
- From trade log to expectancy — 100 trades · 58 wins averaging +$180 · 42 losses averaging −$210
- Conditioning a win rate on a regime flag — P(win) = 0.55 · among winners, 65% occurred with VIX < 15 · among losers, 35% occurred with VIX < 15
- Count outcomes — A fair die has two outcomes greater than 4. Find their probability.
- Sampling error — 100 independent trades have sample SD $10. Estimate SE of the mean.
- Update from counts — Evidence appears in 80 stressed and 180 calm cases. What fraction of these cases are stressed?
- Contract expectancy — A $1 binary payout has probability .7, entry $.62 and total assumed cost $.01. Find expected profit.
Work through the practice exercises · Quant development tools