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Probability & Statistics
Expected value, conditional probability, Bayes
Overview
About probability & statistics questions in quant interviews
Master probability theory, expected-value calculations, conditional probability, and Bayesian inference. The bedrock of quant interviews. Every desk asks them, every textbook starts here.
How to study this topic
A path that works
- 1
Start with the easy set
Warm up with the 15 easy probability & statistics questions. Quick wins build pattern recognition before complexity ramps.
- 2
Drill the medium tier next
42 medium questions sit in the sweet spot where most interview questions cluster. Time yourself, then redo any you missed two days later.
- 3
Stress-test on hard problems
33 hard questions simulate the on-site round. Skip looking at solutions for at least 20 minutes, then write up your approach.
The library
All 90 probability & statistics questions
easyStationarity of a Random WalkeasyPoisson Arrival ProbabilityeasyExponential Distribution MedianeasyVariance of Uniform DistributioneasyCombined Poisson ProcesseseasyType I Error IdentificationeasyVariance of a Geometric Random VariableeasyFair Value: The Six-Sided DieeasyConditional Dice ExpectationeasyImplied Probability: The 3 to 1 RatioeasyCovariance CalculationeasyTwo-Child ProbabilityeasyUnion Bound CalculationeasyIce Cream and Shark AttackseasyGeometric Memorylessness ProofmediumKurtosis and Financial ReturnsmediumDrunk Passenger Seat ProbabilitymediumStick Breaking Triangle ProbabilitymediumDisease Prevalence and Test AccuracymediumCoin Flip VariancemediumBirthday Paradox ThresholdmediumThree Coins: Bayesian InferencemediumExpected Value of Max of Two UniformsmediumDistribution ConvergencemediumThe Noisy Oracle AgreementmediumVolatility of Inverse PricemediumExpected Maximum of Two Uniform VariablesmediumEquity Correlation RiskmediumExpected Empty Bins in Portfolio AllocationmediumBroken Stick TrianglemediumUpdated Coin Bias EstimatemediumMatrix Rank InequalitymediumBertrand's Box SurprisemediumBenford's Law Leading Digit ProbabilitymediumEstimating Fish PopulationmediumMatching Pennies EquilibriummediumLaw of Total VariancemediumMGF Distribution IdentificationmediumProbability Integral Transform DistributionmediumExpected Minimum of Uniform Random VariablesmediumExpected Trades Until 5th WinmediumHypergeometric vs Binomial ProbabilitymediumThe Inclusion-Exclusion TriplemediumThe Convolution ChallengemediumSums of Geometric VariablesmediumThe Chi-Squared OriginmediumSufficient Statistic for Normal MeanmediumMonty Hall GeneralizationmediumPDF Transformation: Squaring a Uniform Random VariablemediumBirthday Attack and Hash CollisionsmediumConditional Expectation Tower PropertymediumIdentifying a Distribution from its PGFmediumExpected Number of Fixed PointsmediumNormal Distribution Fourth MomentmediumJensen's Inequality and Log ReturnsmediumConditional Independence and Marginal IndependencemediumEntropy of a Fair DiehardPalindromic Coin ExpectationhardMaximum of Geometric Variables Asymptotic ExpectationhardCoupon Collector with Unequal ProbabilitieshardLocal Time at Zero of Brownian MotionhardPirate Coin DistributionhardVariance of Integrated Brownian BridgehardOLS HeteroscedasticityhardExpected Dice Rolls to See All FaceshardSemicircle Points ProbabilityhardConsecutive Heads vs TailshardDerangement Probability with EnvelopeshardMarkov Chain Steady StatehardDrunkard's Walk to OriginhardExpected Bins with One BallhardBoy/Girl Paradox (Tuesday Edition)hardCorrelation of Min and Max of UniformshardMeeting ProbabilityhardThe Jacobian TransformhardBallot Counting ProbabilityhardRandom Graph ConnectivityhardThe Two Envelope ParadoxhardBuffon's Needle ProblemhardPolya Urn ConvergencehardLongest Run ExpectationhardLoad Balancing with Two ChoiceshardNon-Transitive DicehardThe Fisher Information BoundhardDrunkard's WalkhardCramér-Rao Lower BoundhardRao-Blackwell ImprovementhardLévy Flight TraderhardExpected Value of the k-th SmallesthardAmoeba Population Extinction
View all 90 probability & statistics questionsRelated topics