Mathematical Statistics 2024
60 questions, booklet MS2024.
Section A · Section A · Q1–30
Practise this section →- 1Cauchy property of two sequencesSequences and SeriesSequences and Series of real numbersEasy
- 2Critical points of a quarticCalculusMultivariate DistributionsMedium
- 3Sum of inverse and inverse adjointMatrices and DeterminantsMatrices and DeterminantsMedium
- 4No blue balls in three drawsDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 5Upper bound for the third quartileUnivariate DistributionsUnivariate DistributionsHard
- 6Linear images of a uniform lawUnivariate DistributionsUnivariate DistributionsEasy
- 7Expectation of a two-point Poisson mapUnivariate DistributionsUnivariate DistributionsEasy
- 8Limit law of the uniform minimumLimit TheoremsLimit TheoremsMedium
- 9Chi-square from paired Gaussian differencesSampling DistributionsSampling DistributionsMedium
- 10Critical value of a Gaussian LRTTesting of HypothesesTesting of HypothesesMedium
- 11Absolute convergence of two trigonometric seriesSequences and SeriesTesting of HypothesesMedium
- 12Continuity of two oscillatory functionsCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 13Partial derivative of an absolute productCalculusMultivariate DistributionsMedium
- 14Local extrema of a strictly convex functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 15Convergence of two improper integralsCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 16Rank and solvability of a 3 by 5 systemMatrices and DeterminantsMatrices and DeterminantsHard
- 17Which collection is an algebraDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 18Pairwise but not mutual independenceDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityHard
- 19Variance of a two-component Gaussian mixtureUnivariate DistributionsUnivariate DistributionsEasy
- 20Which function is a cdfUnivariate DistributionsUnivariate DistributionsHard
- 21Fourth moment of a symmetric square-root chi-squareUnivariate DistributionsUnivariate DistributionsMedium
- 22Variance of an exponential-normal sumMultivariate DistributionsMultivariate DistributionsMedium
- 23Covariance under a triangular joint densityMultivariate DistributionsMultivariate DistributionsMedium
- 24Variance of the difference of sample meansMultivariate DistributionsMultivariate DistributionsEasy
- 25CLT limit of two binomial probabilitiesLimit TheoremsLimit TheoremsHard
- 26A Student ratio from two independent samplesSampling DistributionsSampling DistributionsMedium
- 27Which variance claim fails for two unbiased estimatorsEstimationEstimationHard
- 28MLE of binomial n and p on a gridEstimationEstimationHard
- 29MP test for an exponential rateTesting of HypothesesTesting of HypothesesMedium
- 30Power interval of a chi-square scale testTesting of HypothesesTesting of HypothesesMedium
Section B · Section B · Q31–40
Practise this section →- 31Convergence of a recursively defined seriesSequences and SeriesTesting of HypothesesHard
- 32Mean value conclusions from four function valuesCalculusDifferential Calculus of one and two real variables, and Integral CalculusHard
- 33Eigenvalues of A and of A plus A squaredMatrices and DeterminantsMatrices and DeterminantsMedium
- 34Comparisons of four labelled diceDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityHard
- 35Consequences of an even densityUnivariate DistributionsUnivariate DistributionsMedium
- 36Min and max of independent binomialsUnivariate DistributionsUnivariate DistributionsMedium
- 37Probabilities under an ordered exponential densityMultivariate DistributionsMultivariate DistributionsHard
- 38Always-true properties of sample mean and varianceLimit TheoremsLimit TheoremsMedium
- 39t and F statistics from even and odd observationsSampling DistributionsSampling DistributionsHard
- 40Size, power and UMP property for a normal meanTesting of HypothesesTesting of HypothesesMedium
Section C · Section C · Q41–60
Practise this section →- 41Radius of a shifted power seriesSequences and SeriesSequences and Series of real numbersEasy
- 42Turning point of an integral functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 43Dimension of equal first two coordinatesMatrices and DeterminantsMatrices and DeterminantsEasy
- 44Probability of at least two sixesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 45A linear combination of binomial mean and varianceUnivariate DistributionsUnivariate DistributionsEasy
- 46Probability that a truncated Cauchy average is largeLimit TheoremsLimit TheoremsHard
- 47Probability limit of reciprocal F variablesSampling DistributionsSampling DistributionsMedium
- 48Expected maximum of exponential transformsUnivariate DistributionsUnivariate DistributionsEasy
- 49Expected sample minimum of a heavy-tailed densityUnivariate DistributionsUnivariate DistributionsMedium
- 50UMVUE of an exponential meanEstimationEstimationEasy
- 51A scaled sine-exponential limitCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Integral of radius over a circular sectorCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 53Linear combination of orthogonal-matrix entriesMatrices and DeterminantsMatrices and DeterminantsMedium
- 54Conditional defectives from a random factoryDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 55A discrete probability on five atomsUnivariate DistributionsUnivariate DistributionsEasy
- 56Expected gain in a coin-toss lotteryUnivariate DistributionsUnivariate DistributionsEasy
- 57Correlation of cosine and sineMultivariate DistributionsMultivariate DistributionsEasy
- 58MLE of a symmetric uniform half-widthEstimationEstimationEasy
- 59Width of a t confidence intervalSampling DistributionsSampling DistributionsMedium
- 60Power of a Poisson sum testTesting of HypothesesTesting of HypothesesMedium