Mathematical Statistics 2020
60 questions, booklet MS2020.
Section A · Section A · Q1–30
Practise this section →- 1Ratio limit implies unboundednessSequences and SeriesSequences and Series of real numbersEasy
- 2Differentiability determines two constantsCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 3Area between a quartic and a parabolaCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 4Unique solution among parameter pairsMatrices and DeterminantsMatrices and DeterminantsMedium
- 5A Frechet bound stated backwardsDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 6Poisson reciprocal expectationUnivariate DistributionsUnivariate DistributionsMedium
- 7Chebyshev bound for pony weightsUnivariate DistributionsUnivariate DistributionsEasy
- 8Variance of a normal sample varianceSampling DistributionsSampling DistributionsEasy
- 9CLT for pairwise differencesLimit TheoremsLimit TheoremsMedium
- 10Pairwise-difference estimator of the varianceEstimationEstimationMedium
- 11Limit of a two-term average recurrenceSequences and SeriesSequences and Series of real numbersMedium
- 12Identifying the only convergent seriesSequences and SeriesSequences and Series of real numbersMedium
- 13Alpha and beta from a limitCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 14Cubics over quadratics at the originCalculusDifferential Calculus of one and two real variables, and Integral CalculusHard
- 15Iterated limits for a paraboloid solidCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 16Polar double integral over a shifted discCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 17Linear transformation on three anchor vectorsMatrices and DeterminantsMatrices and DeterminantsEasy
- 18Cayley transform of a skew-symmetric matrixMatrices and DeterminantsMatrices and DeterminantsMedium
- 19Three defective firecrackers in a rowDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 20Ranking probability of two order constraintsSampling DistributionsSampling DistributionsMedium
- 21Least squares from five summary sumsEstimationEstimationMedium
- 22Two-squares chi-square tail probabilitySampling DistributionsSampling DistributionsEasy
- 23Waiting for the second successUnivariate DistributionsUnivariate DistributionsMedium
- 24Probability that half of Y exceeds XMultivariate DistributionsMultivariate DistributionsMedium
- 25Expectation of a chi-square ratioSampling DistributionsSampling DistributionsHard
- 26Student t from two independent samplesSampling DistributionsSampling DistributionsMedium
- 27The estimator that is not an MLEEstimationEstimationHard
- 28Chi-square pivot for an exponential rateEstimationEstimationMedium
- 29Consistency limit equals a logLimit TheoremsLimit TheoremsMedium
- 30UMP test for a Beta familyTesting of HypothesesTesting of HypothesesHard
Section B · Section B · Q31–40
Practise this section →- 31Limsup and liminf of a periodic sineSequences and SeriesSequences and Series of real numbersMedium
- 32Two saddles among four critical pointsCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 33Arc length integrals for a parabolaCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 34Orthogonal completion of a two-by-two matrixMatrices and DeterminantsMatrices and DeterminantsMedium
- 35Four Bernoulli waiting-time factsUnivariate DistributionsUnivariate DistributionsEasy
- 36Moments of a binomial mixtureMultivariate DistributionsMultivariate DistributionsHard
- 37Student t and F from three normalsSampling DistributionsSampling DistributionsMedium
- 38Laws of large numbers for indicatorsLimit TheoremsLimit TheoremsMedium
- 39Sample mean beats sample variance for PoissonEstimationEstimationHard
- 40Neyman-Pearson test at a named sizeTesting of HypothesesTesting of HypothesesMedium
Section C · Section C · Q41–60
Practise this section →- 41Radical limit by dominant powersSequences and SeriesSequences and Series of real numbersEasy
- 42Global maximum of a rational functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 43Iterated exponential integral by swapping orderCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 44Rank of a four-by-four matrixMatrices and DeterminantsMatrices and DeterminantsMedium
- 45Conditional mean on a triangular stripMultivariate DistributionsMultivariate DistributionsMedium
- 46Geometric-thinned Poisson total probabilityDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 47Normal combination tail probabilityUnivariate DistributionsUnivariate DistributionsMedium
- 48F-quantile reciprocitySampling DistributionsSampling DistributionsEasy
- 49Invariance for an exponential functionalEstimationEstimationMedium
- 50Error probabilities of a uniform testTesting of HypothesesTesting of HypothesesMedium
- 51Pinned down by the derivative boundCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52A Maclaurin coefficient matchingSequences and SeriesSequences and Series of real numbersMedium
- 53Trace of a cube under similarityMatrices and DeterminantsMatrices and DeterminantsMedium
- 54Matrix polynomials through eigenvaluesMatrices and DeterminantsMatrices and DeterminantsMedium
- 55Binomial MGFs and a small convolutionUnivariate DistributionsUnivariate DistributionsMedium
- 56Fractional part of a uniform variableUnivariate DistributionsUnivariate DistributionsEasy
- 57Two printers and a fast jobDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 58UMVUE of a Bernoulli polynomialEstimationEstimationMedium
- 59UMVUE of a Poisson tailEstimationEstimationHard
- 60Power of the two-sided normal LRTTesting of HypothesesTesting of HypothesesMedium