Lilly Tech Systems
Probability & Statistics Coding
The statistics coding problems that quant firms, hedge funds, and top data science teams actually ask. Every solution implements the method from scratch — no scipy.stats, no statsmodels. You will build descriptive statistics, probability distributions, hypothesis tests, Monte Carlo simulations, and Bayesian inference using only Python and basic math.
Your Learning Path
Follow these lessons in order for complete preparation, or jump to any topic. Every problem implements the statistical method from scratch.
1. Stats Coding in Interviews
What to expect at quant firms and data science roles, scipy vs from scratch, common patterns, and how interviewers evaluate statistical fluency.
2. Descriptive Statistics
6 problems: mean/median/mode, variance/std, percentiles, histogram, correlation, and running statistics — all implemented from scratch.
3. Implement Distributions
5 problems: normal distribution PDF/CDF, binomial PMF, Poisson distribution, exponential distribution, and sampling methods (inverse CDF, Box-Muller).
4. Hypothesis Testing in Code
5 problems: t-test, chi-squared test, A/B test significance, permutation test, and bootstrap confidence intervals — coded from first principles.
5. Monte Carlo Simulation
5 problems: estimate pi, option pricing (Black-Scholes), probability puzzles via simulation, random walk analysis, and Markov chain Monte Carlo.
6. Bayesian Methods in Code
5 problems: Bayesian inference engine, Beta-Binomial model, Naive Bayes classifier, Bayesian A/B test, and Thompson sampling — all from scratch.
7. Patterns & Tips
Statistical coding patterns, numerical precision pitfalls, interview strategy, and FAQ with detailed answers for probability & statistics questions.
What You'll Learn
By the end of this course, you will be able to:
Implement Stats from Scratch
Build mean, variance, t-tests, chi-squared tests, and confidence intervals without any library calls. The skill quant firms test above all else.
Code Probability Distributions
Implement normal, binomial, Poisson, and exponential distributions from their mathematical definitions. Generate samples using inverse CDF and Box-Muller.
Simulate & Estimate
Use Monte Carlo methods to estimate probabilities, price options, solve puzzles, and run MCMC samplers. The backbone of quantitative finance.
Think Bayesian
Build Bayesian inference engines, implement Naive Bayes from scratch, and run Thompson sampling for bandit problems. The modern approach to uncertainty.