Mathematical Statistics 2025
60 questions, booklet MS2025.
Section A · Section A · Q1–30
Practise this section →- 1Floor sequence and fractional partSequences and SeriesSequences and Series of real numbersEasy
- 2Real characteristic roots of a circulantMatrices and DeterminantsMatrices and DeterminantsMedium
- 3Integral of an odd periodic functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 4Variance of a split Bernoulli inner productMultivariate DistributionsMultivariate DistributionsEasy
- 5Power of an MP Bernoulli testTesting of HypothesesTesting of HypothesesMedium
- 6Expectation of a signed Poisson multipleUnivariate DistributionsUnivariate DistributionsEasy
- 7CLT for the Bernoulli MLELimit TheoremsLimit TheoremsMedium
- 8Power of MP test of uniform vs triangularTesting of HypothesesTesting of HypothesesMedium
- 9Probability for a weighted sum of GaussiansUnivariate DistributionsUnivariate DistributionsEasy
- 10Confidence interval for a triangular scaleEstimationEstimationHard
- 11Roots of x plus pi cos xCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 12Maximum of three dice equals fourDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 13A rank statement that can failMatrices and DeterminantsMatrices and DeterminantsHard
- 14Dimensions of successive imagesMatrices and DeterminantsMatrices and DeterminantsHard
- 15Darboux property versus continuityCalculusDifferential Calculus of one and two real variables, and Integral CalculusHard
- 16Nonsingularity from an annihilating polynomialMatrices and DeterminantsMatrices and DeterminantsMedium
- 17Independence properties of sum and differenceMultivariate DistributionsMultivariate DistributionsMedium
- 18Expected area of a random circular triangleDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 19Parity of a uniform-binomial mixtureUnivariate DistributionsUnivariate DistributionsMedium
- 20Cdf of a censored exponentialUnivariate DistributionsUnivariate DistributionsMedium
- 21Constant matching a chi-five expectationSampling DistributionsSampling DistributionsMedium
- 22UMP test for a Laplace scaleTesting of HypothesesTesting of HypothesesHard
- 23Correlation of two lognormalsMultivariate DistributionsMultivariate DistributionsMedium
- 24Limit of a self-normalised uniform sumLimit TheoremsLimit TheoremsMedium
- 25Exponential moment of a Gaussian productMultivariate DistributionsMultivariate DistributionsMedium
- 26Ancillary statistics for a correlationEstimationEstimationHard
- 27UMVUE in a three-cell multinomialEstimationEstimationHard
- 28Variance of the t ratio Xbar over SSampling DistributionsSampling DistributionsMedium
- 29Poisson approximation on a diskLimit TheoremsLimit TheoremsMedium
- 30A condition for binomials to go to zeroLimit TheoremsLimit TheoremsMedium
Section B · Section B · Q31–40
Practise this section →- 31A Babylonian recurrence starting negativeSequences and SeriesSequences and Series of real numbersHard
- 32How many parameter pairs give infinite solutionsMatrices and DeterminantsMatrices and DeterminantsHard
- 33Decay of a positive function at infinityCalculusDifferential Calculus of one and two real variables, and Integral CalculusHard
- 34Moments from a squared trinomial mgfMultivariate DistributionsMultivariate DistributionsMedium
- 35A linear joint density on the unit squareMultivariate DistributionsMultivariate DistributionsMedium
- 36t and F pivots from a normal sampleSampling DistributionsSampling DistributionsHard
- 37Estimators when mean equals varianceEstimationEstimationHard
- 38Sufficiency for a power familyEstimationEstimationMedium
- 39Least squares with a balanced plus-minus designEstimationEstimationHard
- 40Geometric MOM estimatorEstimationEstimationMedium
Section C · Section C · Q41–60
Practise this section →- 41L1 norm of characteristic coefficientsMatrices and DeterminantsMatrices and DeterminantsEasy
- 42Radius of n-factorial over n to the nSequences and SeriesSequences and Series of real numbersEasy
- 43Second-order difference of a sineCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 44Constant in a paired-difference variance estimatorLimit TheoremsEstimationEasy
- 45Type I error of a uniform max testTesting of HypothesesTesting of HypothesesEasy
- 46MLE of lambda in a Poisson mixtureEstimationEstimationHard
- 47Mean of the minimum of two ParetosUnivariate DistributionsUnivariate DistributionsEasy
- 48A probability in an ordered tripleMultivariate DistributionsMultivariate DistributionsMedium
- 49Uniform Irwin-Hall versus a coin tossDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 50Exactly two pairs among five shoesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 51Closest point on a circle to (1,2)CalculusMultivariate DistributionsEasy
- 52Area between a cubic and the line y=xCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 53Volume of a truncated ellipsoidCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 54MOM from summed squared distancesEstimationEstimationMedium
- 55Waiting time for two heads in a rowStochastic ProcessesStochastic ProcessesEasy
- 56Third moment from a tight fourth momentUnivariate DistributionsUnivariate DistributionsMedium
- 57UMVUE of theta squared for a ParetoEstimationEstimationHard
- 58Conditional mean on the left halfUnivariate DistributionsUnivariate DistributionsEasy
- 59Probability the second order statistic exceeds the medianSampling DistributionsSampling DistributionsEasy
- 60Gaussian covariance against a cubicMultivariate DistributionsMultivariate DistributionsMedium