Mathematical Statistics 2026
60 questions, booklet MS2026.
Section A · Section A · Q1–30
Practise this section →- 1Radius of a squared factorial seriesSequences and SeriesSequences and Series of real numbersMedium
- 2Integral function critical pointsCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 3Definiteness from trace and determinantMatrices and DeterminantsMatrices and DeterminantsEasy
- 4Jacobian of fourth-power inverseUnivariate DistributionsUnivariate DistributionsEasy
- 5Bayes probability for premium teaDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 6Uncorrelated linear combinationsMultivariate DistributionsMultivariate DistributionsMedium
- 7Sufficient statistic for normal varianceEstimationEstimationEasy
- 8Power function of a two-sided LRTTesting of HypothesesTesting of HypothesesMedium
- 9Two-state chain stationary distributionStochastic ProcessesStochastic ProcessesEasy
- 10Student t from an extra normalSampling DistributionsSampling DistributionsEasy
- 11Limsup along even indicesSequences and SeriesSequences and Series of real numbersHard
- 12Piecewise function differentiabilityCalculusDifferential Calculus of one and two real variables, and Integral CalculusHard
- 13Saddle points of xy(5x+3y-6)CalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 14Continuity versus partials off axesCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 15Washer volume of a parabolic regionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 16Skew-symmetric orthogonal matricesMatrices and DeterminantsMatrices and DeterminantsEasy
- 17Comparing CV and sample SDDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 18Probability a random matrix is orthogonalMatrices and DeterminantsMatrices and DeterminantsHard
- 19Conditional inequalities and independenceDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 20Variance from a Poisson MGFUnivariate DistributionsUnivariate DistributionsEasy
- 21Mean of a Rayleigh random variableUnivariate DistributionsUnivariate DistributionsMedium
- 22Component failure order probabilityMultivariate DistributionsMultivariate DistributionsHard
- 23Convergence in probability not L2Limit TheoremsLimit TheoremsMedium
- 24MLE in an exponential-of-exponential modelEstimationEstimationMedium
- 25Invariance for exponential functionalsEstimationEstimationMedium
- 26Error probabilities for a chi-square testTesting of HypothesesTesting of HypothesesMedium
- 27Power of a uniform threshold testTesting of HypothesesTesting of HypothesesMedium
- 28Runs test for AQI signsNonparametric MethodsTesting of HypothesesMedium
- 29Recurrent class in a three-state chainStochastic ProcessesStochastic ProcessesMedium
- 30F and Cauchy from independent normalsSampling DistributionsSampling DistributionsMedium
Section B · Section B · Q31–40
Practise this section →- 31Recurrence around the fixed point 2Sequences and SeriesSequences and Series of real numbersMedium
- 32Rank facts for rectangular matricesMatrices and DeterminantsMatrices and DeterminantsMedium
- 33Summary statistics of eleven lifetimesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 34Which set functions are probabilitiesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityHard
- 35Square and reciprocal transformationsUnivariate DistributionsUnivariate DistributionsHard
- 36Marginals of x exp(-x(y+1))Multivariate DistributionsMultivariate DistributionsMedium
- 37UMVUE of an exponential tailEstimationEstimationHard
- 38OLS identities for five design pointsEstimationEstimationHard
- 39MP test for two geometric samplesTesting of HypothesesTesting of HypothesesHard
- 40Laws of a gamma sum of exponentialsSampling DistributionsSampling DistributionsMedium
Section C · Section C · Q41–60
Practise this section →- 41Taylor coefficients of 3 e^x cos 2xCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 42Parameter sum for infinite solutionsMatrices and DeterminantsMatrices and DeterminantsEasy
- 43Corrected Spearman correlationDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 44Closer to centre than to cornersDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 45Chebyshev bound on a six-sigma intervalUnivariate DistributionsUnivariate DistributionsEasy
- 46Correlation from a conditional intervalMultivariate DistributionsMultivariate DistributionsMedium
- 47WLLN for squares of U(0,3)Limit TheoremsLimit TheoremsEasy
- 48MOM estimate of a Beta shapeEstimationEstimationMedium
- 49Expectation of a Poisson productStochastic ProcessesStochastic ProcessesEasy
- 50P(max of three U(1,2) exceeds 1.5)Sampling DistributionsSampling DistributionsEasy
- 51Area between parabola and lineCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Determinant via column operationsMatrices and DeterminantsMatrices and DeterminantsHard
- 53Four dice summing to fourteenDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 54Cubic in the median of X-1Univariate DistributionsUnivariate DistributionsMedium
- 55Conditional variance in a joint pmfMultivariate DistributionsMultivariate DistributionsHard
- 56CLT for a drifting intervalLimit TheoremsLimit TheoremsMedium
- 57Sample size for a fixed-width intervalEstimationEstimationMedium
- 58p-value for a Beta shape testTesting of HypothesesTesting of HypothesesHard
- 59Sign-test p-value plus accept indicatorNonparametric MethodsTesting of HypothesesMedium
- 60Expectation involving the sample medianSampling DistributionsSampling DistributionsHard