Master probability and statistics with our comprehensive collection of 100+ practice problems, step-by-step solutions, and real interview questions from Jane Street, Citadel, Two Sigma, and other top quantitative trading firms.
Fundamental probability concepts, sample spaces, and basic calculations.
Bayes' theorem, independence, and conditional probability applications.
Common probability distributions and their applications in finance.
Expected value calculations, variance, and risk assessment.
Statistical hypothesis testing and significance testing.
Linear regression, correlation, and statistical modeling.
You flip a fair coin 10 times. What's the probability of getting exactly 7 heads?
Use binomial probability: P(X=7) = C(10,7) × (0.5)^7 × (0.5)^3 = 120 × (0.5)^10 = 120/1024 ≈ 0.117
A disease affects 1% of the population. A test is 99% accurate for both positive and negative cases. If someone tests positive, what's the probability they actually have the disease?
P(Disease|Positive) = P(Positive|Disease) × P(Disease) / P(Positive) = 0.99 × 0.01 / (0.99 × 0.01 + 0.01 × 0.99) = 0.5
You roll a die until you get a 6. What's the expected number of rolls?
E[X] = 1/p = 1/(1/6) = 6 rolls. This is the expected value of a geometric distribution.
Focus on conditional probability, Bayes' theorem, expected value calculations, common distributions (normal, binomial, Poisson), and basic combinatorics. These topics appear in 80% of quant interviews.
Start by clearly defining the sample space and events. Use systematic approaches like tree diagrams or Bayes' theorem. Always explain your reasoning step by step and check your answer makes intuitive sense.
Practice with real interview questions from top firms. Focus on understanding the underlying concepts rather than memorizing formulas. Time yourself to simulate interview pressure and practice explaining solutions out loud.