Multivariate Distributions
69 questions across 10 topics.
Multivariate Distributions
- 6Uncorrelated linear combinationsIIT JAM 2026 MSMultivariate DistributionsMedium
- 22Component failure order probabilityIIT JAM 2026 MSMultivariate DistributionsHard
- 36Marginals of x exp(-x(y+1))IIT JAM 2026 MSMultivariate DistributionsMedium
- 46Correlation from a conditional intervalIIT JAM 2026 MSMultivariate DistributionsMedium
- 55Conditional variance in a joint pmfIIT JAM 2026 MSMultivariate DistributionsHard
- 4Variance of a split Bernoulli inner productIIT JAM 2025 MSMultivariate DistributionsEasy
- 17Independence properties of sum and differenceIIT JAM 2025 MSMultivariate DistributionsMedium
- 23Correlation of two lognormalsIIT JAM 2025 MSMultivariate DistributionsMedium
- 25Exponential moment of a Gaussian productIIT JAM 2025 MSMultivariate DistributionsMedium
- 34Moments from a squared trinomial mgfIIT JAM 2025 MSMultivariate DistributionsMedium
- 35A linear joint density on the unit squareIIT JAM 2025 MSMultivariate DistributionsMedium
- 48A probability in an ordered tripleIIT JAM 2025 MSMultivariate DistributionsMedium
- 60Gaussian covariance against a cubicIIT JAM 2025 MSMultivariate DistributionsMedium
- 22Variance of an exponential-normal sumIIT JAM 2024 MSMultivariate DistributionsMedium
- 23Covariance under a triangular joint densityIIT JAM 2024 MSMultivariate DistributionsMedium
- 24Variance of the difference of sample meansIIT JAM 2024 MSMultivariate DistributionsEasy
- 37Probabilities under an ordered exponential densityIIT JAM 2024 MSMultivariate DistributionsHard
- 57Correlation of cosine and sineIIT JAM 2024 MSMultivariate DistributionsEasy
- 17Probability on parabolic domainIIT JAM 2023 MSMultivariate DistributionsMedium
- 21Expectation of minimum in piecewise densityIIT JAM 2023 MSMultivariate DistributionsMedium
- 29Probabilities of Poisson-gamma mixtureIIT JAM 2023 MSMultivariate DistributionsMedium
- 34Moments of symmetric trinomial distributionIIT JAM 2023 MSMultivariate DistributionsMedium
- 52Conditional variance in bivariate normalIIT JAM 2023 MSMultivariate DistributionsEasy
- 60Probability exactly two normals below thresholdIIT JAM 2023 MSMultivariate DistributionsMedium
- 7Expected value in a bivariate densityIIT JAM 2022 MSMultivariate DistributionsEasy
- 22Expectation of log uniform ratioIIT JAM 2022 MSMultivariate DistributionsMedium
- 23Conditional probability in bivariate normalIIT JAM 2022 MSMultivariate DistributionsMedium
- 36Independence and distribution of normal sumsIIT JAM 2022 MSMultivariate DistributionsMedium
- 44Probability between power and linear boundsIIT JAM 2022 MSMultivariate DistributionsEasy
- 47Probability of absolute sum of discrete variablesIIT JAM 2022 MSMultivariate DistributionsEasy
- 6Correlation between X and its squareIIT JAM 2021 MSMultivariate DistributionsMedium
- 21Variance from a joint MGFIIT JAM 2021 MSMultivariate DistributionsMedium
- 52Covariance inside a parabolic stripIIT JAM 2021 MSMultivariate DistributionsMedium
- 53Correlation of sign-flipped normalsIIT JAM 2021 MSMultivariate DistributionsHard
- 56Factored binomial joint pmfIIT JAM 2021 MSMultivariate DistributionsMedium
- 24Probability that half of Y exceeds XIIT JAM 2020 MSMultivariate DistributionsMedium
- 36Moments of a binomial mixtureIIT JAM 2020 MSMultivariate DistributionsHard
- 45Conditional mean on a triangular stripIIT JAM 2020 MSMultivariate DistributionsMedium
Conditional expectation
- 26Conditional mean given X exceeds YIIT JAM 2019 MSConditional expectationMedium
- 48Expectation in a two-stage coin tossingIIT JAM 2019 MSConditional expectationMedium
- 57Variance using the law of total varianceIIT JAM 2019 MSConditional expectationHard
- 7Expected ratio of partial sum to totalIIT JAM 2018 MSConditional expectationMedium
- 24Conditional moments given X for a joint densityIIT JAM 2018 MSConditional expectationMedium
- 57Conditional mean on a wedge-shaped supportIIT JAM 2017 MSConditional expectationMedium
- 19Variance of a Poisson variable with an exponential random meanIIT JAM 2015 MSConditional expectationHard
- 51Mean of a variable whose conditional law is uniform on zero to yIIT JAM 2015 MSConditional expectationMedium
Joint densities
- 25Probability that one uniform exceeds the sum of twoIIT JAM 2019 MSJoint densitiesMedium
- 14Mean of a variable from a triangular joint densityIIT JAM 2017 MSJoint densitiesMedium
- 15Probability that a sum exceeds one halfIIT JAM 2017 MSJoint densitiesMedium
- 56Mean of a variable from a factorising joint densityIIT JAM 2016 MSJoint densitiesMedium
- 12Normalising constant for a joint density on a wedgeIIT JAM 2013 MSJoint densitiesMedium
Conditional distributions
- 25Conditional pmf from a joint pmfIIT JAM 2018 MSConditional distributionsEasy
- 44Conditional probability from a pmf with squaresIIT JAM 2017 MSConditional distributionsEasy
- 58Combination of probabilities from conditional informationIIT JAM 2017 MSConditional distributionsMedium
- 11Conditional probability given X from a joint densityIIT JAM 2016 MSConditional distributionsMedium
- 30Variance of a variable from a wedge-shaped joint densityIIT JAM 2014 MSConditional distributionsHard
Correlation and covariance
- 27Correlation for an ordered exponential pairIIT JAM 2018 MSCorrelation and covarianceHard
- 45Nine times a covariance from a triangular densityIIT JAM 2017 MSCorrelation and covarianceHard
- 2Correlation between two overlapping sums of independent normalsIIT JAM 2015 MSCorrelation and covarianceEasy
- 35Matrices that can be a variance-covariance matrixIIT JAM 2015 MSCorrelation and covarianceMedium
- 10Correlation between a sum of two normals and the total of eightIIT JAM 2012 MSCorrelation and covarianceMedium