Mathematical Statistics 2021
60 questions, booklet MS2021.
Section A · Section A · Q1–30
Practise this section →- 1Geometric mean limit via Riemann sumSequences and SeriesSequences and Series of real numbersMedium
- 2Strictly increasing polynomial is bijectiveCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 3Exponentials against a cosineCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 4Half a binomial rowSequences and SeriesSequences and Series of real numbersMedium
- 5CLT for negative log uniformsLimit TheoremsLimit TheoremsMedium
- 6Correlation between X and its squareMultivariate DistributionsMultivariate DistributionsMedium
- 7Eigenvectors must stay independentMatrices and DeterminantsMatrices and DeterminantsMedium
- 8Absolute convergence and one divergent seriesSequences and SeriesSequences and Series of real numbersMedium
- 9Coin-selected urn BayesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 10Odd expectations under LaplaceUnivariate DistributionsUnivariate DistributionsMedium
- 11Cubic-over-quadratic partials at originCalculusDifferential Calculus of one and two real variables, and Integral CalculusHard
- 12CLT for fourth powers of normalsLimit TheoremsLimit TheoremsMedium
- 13Three successes before four failuresUnivariate DistributionsUnivariate DistributionsMedium
- 14Finite moments of a half-Cauchy ratioUnivariate DistributionsUnivariate DistributionsMedium
- 15Random coin tossed five timesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 16Floor of an exponentialUnivariate DistributionsUnivariate DistributionsMedium
- 17Uniform MGF and two probesUnivariate DistributionsUnivariate DistributionsMedium
- 18UMVUE of the Poisson mass at zero times cubeEstimationEstimationHard
- 19MLE for a shifted uniform familyEstimationEstimationHard
- 20Comparing two chi-square tailsSampling DistributionsSampling DistributionsMedium
- 21Variance from a joint MGFMultivariate DistributionsMultivariate DistributionsMedium
- 22Mean from a quadratic CDFUnivariate DistributionsUnivariate DistributionsEasy
- 23Dual exponential tests with flipped hypothesesTesting of HypothesesTesting of HypothesesHard
- 24Two log series coincideSequences and SeriesSequences and Series of real numbersEasy
- 25Conditional inclusion-exclusion with three eventsDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 26Monotone geometric-power recurrenceSequences and SeriesSequences and Series of real numbersMedium
- 27Type II error against a triangular densityTesting of HypothesesTesting of HypothesesMedium
- 28Unique solution through the determinantMatrices and DeterminantsMatrices and DeterminantsMedium
- 29A ratio condition forcing divergenceSequences and SeriesSequences and Series of real numbersMedium
- 30A Bonferroni statement that failsDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
Section B · Section B · Q31–40
Practise this section →- 31An inconsistent system tells the rankMatrices and DeterminantsMatrices and DeterminantsMedium
- 32When every row adds to oneMatrices and DeterminantsMatrices and DeterminantsMedium
- 33Power function of a one-sided normal LRTTesting of HypothesesTesting of HypothesesMedium
- 34Quadratic form on the unit circleMatrices and DeterminantsMatrices and DeterminantsMedium
- 35What twice differentiability buysCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 36Finite moments under a Pareto tailUnivariate DistributionsUnivariate DistributionsMedium
- 37Shrinking urn asymptoticsUnivariate DistributionsUnivariate DistributionsMedium
- 38Statistics for a symmetric uniformEstimationEstimationMedium
- 39UMVUE and MLE of the inverse scaleEstimationEstimationHard
- 40CRLB for cube and reciprocal of thetaEstimationEstimationMedium
Section C · Section C · Q41–60
Practise this section →- 41Eigenvalues from trace and determinantMatrices and DeterminantsMatrices and DeterminantsMedium
- 42Determinant of a quartic matrix polynomialMatrices and DeterminantsMatrices and DeterminantsMedium
- 43Integral over a slanted triangleCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 44Ordered simplex volume weightedCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 45Size and power from a pmf tableTesting of HypothesesTesting of HypothesesEasy
- 46MLE capped by the parameter rangeEstimationEstimationMedium
- 47A long sum of reciprocal rootsSequences and SeriesSequences and Series of real numbersMedium
- 48Fourth moment of a normal mixtureUnivariate DistributionsUnivariate DistributionsMedium
- 49Mean from a finite-support MGFUnivariate DistributionsUnivariate DistributionsEasy
- 50Length of the log-secant curveCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 51Double integral over a slanted parallelogramCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Covariance inside a parabolic stripMultivariate DistributionsMultivariate DistributionsMedium
- 53Correlation of sign-flipped normalsMultivariate DistributionsMultivariate DistributionsHard
- 54Binomial tail asymptoticsSequences and SeriesSequences and Series of real numbersHard
- 55At most two of four eventsDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 56Factored binomial joint pmfMultivariate DistributionsMultivariate DistributionsMedium
- 57Area between sine and cosineCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 58Counting real roots of an eleventh degreeCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 59Exponential limit with a sine twistSequences and SeriesSequences and Series of real numbersEasy
- 60Integral quotient by L'HopitalCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium