Mathematical Statistics 2023
60 questions, booklet MS2023.
Section A · Section A · Q1–30
Practise this section →- 1Subspace containing eigenvector of matrix powerMatrices and DeterminantsMatrices and DeterminantsMedium
- 2Row and column representations of productMatrices and DeterminantsMatrices and DeterminantsEasy
- 3Reciprocal property of Fisher F distributionSampling DistributionsSampling DistributionsEasy
- 4Probability for Fisher F distributionSampling DistributionsSampling DistributionsMedium
- 5Limiting variance of partial uniform sumLimit TheoremsLimit TheoremsEasy
- 6Parameter-free conditional expectation for normalEstimationEstimationMedium
- 7Saddle point of bivariate quadraticCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 8Probability that at least two events occurDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 9Tail integral for second momentDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 10Power of MP test for power-law densityTesting of HypothesesTesting of HypothesesMedium
- 11Distribution of exponential order statisticsSampling DistributionsSampling DistributionsMedium
- 12Covariance and moments of linear transformationUnivariate DistributionsUnivariate DistributionsEasy
- 13Area of random right triangleDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 14CLT constants for scaled discrete variablesLimit TheoremsLimit TheoremsMedium
- 15Limiting probabilities under WLLNLimit TheoremsLimit TheoremsMedium
- 16Number of curve intersectionsCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 17Probability on parabolic domainMultivariate DistributionsMultivariate DistributionsMedium
- 18UMVUE and CRLB for normal parameterEstimationEstimationMedium
- 19Consistency of shifted exponential estimatorsEstimationEstimationMedium
- 20Relations among uniform MOM estimatorsEstimationEstimationMedium
- 21Expectation of minimum in piecewise densityMultivariate DistributionsMultivariate DistributionsMedium
- 22Probability tail from moment sequenceUnivariate DistributionsUnivariate DistributionsMedium
- 23Variance from pmf recurrence relationUnivariate DistributionsUnivariate DistributionsEasy
- 24Monotone convergence of recursive sequenceSequences and SeriesSequences and Series of real numbersMedium
- 25Ratio and root test for seriesSequences and SeriesSequences and Series of real numbersMedium
- 26Volume of truncated cylinderCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 27Parameter values for infinite solutionsMatrices and DeterminantsMatrices and DeterminantsMedium
- 28P-value of two-sided t-testTesting of HypothesesTesting of HypothesesMedium
- 29Probabilities of Poisson-gamma mixtureMultivariate DistributionsMultivariate DistributionsMedium
- 30Closest point on a sphereCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
Section B · Section B · Q31–40
Practise this section →- 31Symmetric and skew-symmetric decomposition propertiesMatrices and DeterminantsMatrices and DeterminantsMedium
- 32Distributions and moments of normal functionsSampling DistributionsSampling DistributionsHard
- 33One-sided and two-sided confidence intervalsEstimationEstimationHard
- 34Moments of symmetric trinomial distributionMultivariate DistributionsMultivariate DistributionsMedium
- 35Adjoint matrix eigenvalues and traceMatrices and DeterminantsMatrices and DeterminantsHard
- 36Differentiability of rational bivariate functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 37Cauchy ratio and F distributionSampling DistributionsSampling DistributionsMedium
- 38Double integral of maximum functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 39Quantiles and Chebyshev bound for ParetoUnivariate DistributionsUnivariate DistributionsMedium
- 40Regression lines and correlation propertiesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
Section C · Section C · Q41–60
Practise this section →- 41Minimum number of roots of second derivativeCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 42Parameter values from degenerate limit CDFLimit TheoremsLimit TheoremsMedium
- 43Limit of integral ratioCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 44Constant for unbiased normal scale estimationEstimationEstimationEasy
- 45Variance of logarithmic transformed variableUnivariate DistributionsUnivariate DistributionsEasy
- 46Quantile parameter of normal linear combinationUnivariate DistributionsUnivariate DistributionsEasy
- 47Conditional probability for telescoping pmfDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 48Sum of arithmetico-geometric seriesSequences and SeriesSequences and Series of real numbersMedium
- 49Bayes theorem for defective ballDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 50P-value for exponential scale testTesting of HypothesesTesting of HypothesesMedium
- 51Limit of sum of derivative quotientsCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Conditional variance in bivariate normalMultivariate DistributionsMultivariate DistributionsEasy
- 53Value of Gaussian integral constantCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 54MLE of gamma population varianceEstimationEstimationMedium
- 55UMVUE of geometric parameter squaredEstimationEstimationHard
- 56Expected value of random sum of BernoullisUnivariate DistributionsUnivariate DistributionsMedium
- 57Fourth moment of gamma sumSampling DistributionsSampling DistributionsMedium
- 58Size of composite hypothesis testTesting of HypothesesTesting of HypothesesMedium
- 59Sum of Type-II error probabilitiesTesting of HypothesesTesting of HypothesesMedium
- 60Probability exactly two normals below thresholdMultivariate DistributionsMultivariate DistributionsMedium