Univariate Distributions
108 questions across 15 topics.
Univariate Distributions
- 4Jacobian of fourth-power inverseIIT JAM 2026 MSUnivariate DistributionsEasy
- 20Variance from a Poisson MGFIIT JAM 2026 MSUnivariate DistributionsEasy
- 21Mean of a Rayleigh random variableIIT JAM 2026 MSUnivariate DistributionsMedium
- 35Square and reciprocal transformationsIIT JAM 2026 MSUnivariate DistributionsHard
- 45Chebyshev bound on a six-sigma intervalIIT JAM 2026 MSUnivariate DistributionsEasy
- 54Cubic in the median of X-1IIT JAM 2026 MSUnivariate DistributionsMedium
- 6Expectation of a signed Poisson multipleIIT JAM 2025 MSUnivariate DistributionsEasy
- 9Probability for a weighted sum of GaussiansIIT JAM 2025 MSUnivariate DistributionsEasy
- 19Parity of a uniform-binomial mixtureIIT JAM 2025 MSUnivariate DistributionsMedium
- 20Cdf of a censored exponentialIIT JAM 2025 MSUnivariate DistributionsMedium
- 47Mean of the minimum of two ParetosIIT JAM 2025 MSUnivariate DistributionsEasy
- 56Third moment from a tight fourth momentIIT JAM 2025 MSUnivariate DistributionsMedium
- 58Conditional mean on the left halfIIT JAM 2025 MSUnivariate DistributionsEasy
- 5Upper bound for the third quartileIIT JAM 2024 MSUnivariate DistributionsHard
- 6Linear images of a uniform lawIIT JAM 2024 MSUnivariate DistributionsEasy
- 7Expectation of a two-point Poisson mapIIT JAM 2024 MSUnivariate DistributionsEasy
- 19Variance of a two-component Gaussian mixtureIIT JAM 2024 MSUnivariate DistributionsEasy
- 20Which function is a cdfIIT JAM 2024 MSUnivariate DistributionsHard
- 21Fourth moment of a symmetric square-root chi-squareIIT JAM 2024 MSUnivariate DistributionsMedium
- 35Consequences of an even densityIIT JAM 2024 MSUnivariate DistributionsMedium
- 36Min and max of independent binomialsIIT JAM 2024 MSUnivariate DistributionsMedium
- 45A linear combination of binomial mean and varianceIIT JAM 2024 MSUnivariate DistributionsEasy
- 48Expected maximum of exponential transformsIIT JAM 2024 MSUnivariate DistributionsEasy
- 49Expected sample minimum of a heavy-tailed densityIIT JAM 2024 MSUnivariate DistributionsMedium
- 55A discrete probability on five atomsIIT JAM 2024 MSUnivariate DistributionsEasy
- 56Expected gain in a coin-toss lotteryIIT JAM 2024 MSUnivariate DistributionsEasy
- 12Covariance and moments of linear transformationIIT JAM 2023 MSUnivariate DistributionsEasy
- 22Probability tail from moment sequenceIIT JAM 2023 MSUnivariate DistributionsMedium
- 23Variance from pmf recurrence relationIIT JAM 2023 MSUnivariate DistributionsEasy
- 39Quantiles and Chebyshev bound for ParetoIIT JAM 2023 MSUnivariate DistributionsMedium
- 45Variance of logarithmic transformed variableIIT JAM 2023 MSUnivariate DistributionsEasy
- 46Quantile parameter of normal linear combinationIIT JAM 2023 MSUnivariate DistributionsEasy
- 56Expected value of random sum of BernoullisIIT JAM 2023 MSUnivariate DistributionsMedium
- 5Validity of a moment generating functionIIT JAM 2022 MSUnivariate DistributionsEasy
- 6Expectation of reciprocal binomialIIT JAM 2022 MSUnivariate DistributionsEasy
- 8Minimum of two geometric variablesIIT JAM 2022 MSUnivariate DistributionsEasy
- 21Optimal inventory under exponential demandIIT JAM 2022 MSUnivariate DistributionsMedium
- 35Distribution of capped insurance payoutIIT JAM 2022 MSUnivariate DistributionsMedium
- 46Variance of scaled insurance paymentIIT JAM 2022 MSUnivariate DistributionsEasy
- 55Expectation of quadratic polynomial densityIIT JAM 2022 MSUnivariate DistributionsMedium
- 10Odd expectations under LaplaceIIT JAM 2021 MSUnivariate DistributionsMedium
- 13Three successes before four failuresIIT JAM 2021 MSUnivariate DistributionsMedium
- 14Finite moments of a half-Cauchy ratioIIT JAM 2021 MSUnivariate DistributionsMedium
- 16Floor of an exponentialIIT JAM 2021 MSUnivariate DistributionsMedium
- 17Uniform MGF and two probesIIT JAM 2021 MSUnivariate DistributionsMedium
- 22Mean from a quadratic CDFIIT JAM 2021 MSUnivariate DistributionsEasy
- 36Finite moments under a Pareto tailIIT JAM 2021 MSUnivariate DistributionsMedium
- 37Shrinking urn asymptoticsIIT JAM 2021 MSUnivariate DistributionsMedium
- 48Fourth moment of a normal mixtureIIT JAM 2021 MSUnivariate DistributionsMedium
- 49Mean from a finite-support MGFIIT JAM 2021 MSUnivariate DistributionsEasy
- 6Poisson reciprocal expectationIIT JAM 2020 MSUnivariate DistributionsMedium
- 7Chebyshev bound for pony weightsIIT JAM 2020 MSUnivariate DistributionsEasy
- 23Waiting for the second successIIT JAM 2020 MSUnivariate DistributionsMedium
- 35Four Bernoulli waiting-time factsIIT JAM 2020 MSUnivariate DistributionsEasy
- 47Normal combination tail probabilityIIT JAM 2020 MSUnivariate DistributionsMedium
- 55Binomial MGFs and a small convolutionIIT JAM 2020 MSUnivariate DistributionsMedium
- 56Fractional part of a uniform variableIIT JAM 2020 MSUnivariate DistributionsEasy
Continuous distributions
- 24Variance of a beta distributionIIT JAM 2019 MSContinuous distributionsHard
- 44Value of a beta integralIIT JAM 2018 MSContinuous distributionsEasy
- 55Probability from a piecewise density with unknown powerIIT JAM 2018 MSContinuous distributionsHard
- 5Interval probability from a two-piece densityIIT JAM 2017 MSContinuous distributionsEasy
- 55Probability from a piecewise-linear density with unknown middle heightIIT JAM 2017 MSContinuous distributionsMedium
- 58Probability that the square of a variable lies in an intervalIIT JAM 2016 MSContinuous distributionsMedium
- 52Probability from a density with a flat part and a power tailIIT JAM 2015 MSContinuous distributionsMedium
Distribution functions
- 35Interval probabilities from a cdf with jumpsIIT JAM 2019 MSDistribution functionsMedium
- 6Point masses and tail of a mixed distributionIIT JAM 2018 MSDistribution functionsMedium
- 36Probabilities and mean from a step distribution functionIIT JAM 2017 MSDistribution functionsMedium
- 16Expectation from a piecewise cumulative distribution functionIIT JAM 2016 MSDistribution functionsMedium
- 40Properties of a distribution function with a jump and a continuous partIIT JAM 2016 MSDistribution functionsMedium
- 55Conditional probability of an atom from a mixed distribution functionIIT JAM 2015 MSDistribution functionsMedium
- 14Interval probability from a mixed distribution functionIIT JAM 2014 MSDistribution functionsMedium
Mathematical expectation and moments
- 22Mean and tail of a logistic variableIIT JAM 2019 MSMathematical expectation and momentsMedium
- 56Second moment of a piecewise densityIIT JAM 2019 MSMathematical expectation and momentsMedium
- 7Existence of a second moment for a power-law tailIIT JAM 2016 MSMathematical expectation and momentsHard
- 44Expected absolute value of a Laplace variableIIT JAM 2015 MSMathematical expectation and momentsMedium
- 10Sign of the mean of a skew-normal densityIIT JAM 2013 MSMathematical expectation and momentsHard
Poisson distribution
- 7Poisson parameter from a pmf relationIIT JAM 2019 MSPoisson distributionMedium
- 23Poisson approximation for failing bulbsIIT JAM 2019 MSPoisson distributionMedium
- 22Expected factorial of a shifted Poisson variableIIT JAM 2018 MSPoisson distributionMedium
- 5Probability at most one from a Poisson mgfIIT JAM 2016 MSPoisson distributionEasy
Exponential distribution
- 36Positive part of a difference of exponentialsIIT JAM 2019 MSExponential distributionMedium
- 56Tail of the minimum of exponentials beyond mean plus sdIIT JAM 2017 MSExponential distributionMedium
- 41Mean of the minimum of two independent exponentialsIIT JAM 2015 MSExponential distributionEasy
- 13Survival probability of a series system of exponential and gamma lifetimesIIT JAM 2014 MSExponential distributionMedium
Moment generating functions
- 20Mean and variance from a product mgfIIT JAM 2018 MSMoment generating functionsHard
- 6Tail probability from a binomial mgfIIT JAM 2017 MSMoment generating functionsMedium
- 4Moment generating function from a pmf proportional to binomial coefficientsIIT JAM 2015 MSMoment generating functionsEasy
- 3Probability from a normal moment generating functionIIT JAM 2014 MSMoment generating functionsEasy
Normal distribution
- 23Sign of a cubic in a standard normal variableIIT JAM 2018 MSNormal distributionMedium
- 42Probability from a base ten lognormal variableIIT JAM 2017 MSNormal distributionMedium
- 17Normalising constant and shift of a Gaussian-type densityIIT JAM 2015 MSNormal distributionMedium
- 46Location of the interval of fixed length with maximum normal probabilityIIT JAM 2015 MSNormal distributionMedium