Mathematical Statistics 2014
35 questions, booklet MS2014.
Section A · Section A · Q1–35
Practise this section →- 1Roots of a cubic equation in an interval via Rolle's theoremCalculusDifferential calculus of one variableHard
- 2Probability that a circle of uniform radius has small areaDescriptive Statistics and ProbabilityProbabilityEasy
- 3Probability from a normal moment generating functionUnivariate DistributionsMoment generating functionsEasy
- 4Number of components in a parallel systemDescriptive Statistics and ProbabilityProbabilityEasy
- 5Nature of an upper triangular matrix with distinct diagonalMatrices and DeterminantsProperties of matricesMedium
- 6Which maps of three-space are linearMatrices and DeterminantsLinear transformationsEasy
- 7Matrix of a linear transformation in a given basisMatrices and DeterminantsLinear transformationsHard
- 8Independent pairs built from independent random variablesDescriptive Statistics and ProbabilityProbabilityMedium
- 9Convergence of a logarithmic series with a parameterSequences and SeriesConvergence of seriesMedium
- 10Critical value of the most powerful test for a Pareto-type densityTesting of HypothesesMost powerful testsHard
- 11Power of the most powerful test for two densities on the unit intervalTesting of HypothesesMost powerful testsMedium
- 12Completeness of two statistics with one-parameter pmfsEstimationSufficiency and completenessHard
- 13Survival probability of a series system of exponential and gamma lifetimesUnivariate DistributionsExponential distributionMedium
- 14Interval probability from a mixed distribution functionUnivariate DistributionsDistribution functionsMedium
- 15Probability that the last of four players first rolls a sixDescriptive Statistics and ProbabilityProbabilityMedium
- 16Type of the critical point of a cubic polynomial in two variablesCalculusDifferential calculus of two variablesHard
- 17Area between a line and an absolute-value parabolaCalculusIntegral calculusMedium
- 18Limit of a probability for a sum of uniform variablesLimit TheoremsCentral Limit Theorem (i.i.d. and finite variance case)Medium
- 19Tail probability of a linear combination of correlated standard normalsMultivariate DistributionsBivariate normal distributionMedium
- 20Probability that a ball drawn after a random transfer is whiteDescriptive Statistics and ProbabilityProbabilityMedium
- 21Order of integration after switching for a region between a parabola and a lineCalculusIntegral calculusMedium
- 22Parameter values for which a linear system has infinitely many solutionsMatrices and DeterminantsSystems of linear equationsMedium
- 23Differential equation with two prescribed exponential solutionsDifferential EquationsGeneral theory of linear ODEsHard
- 24Behaviour of the averaged partial sums of the harmonic-root seriesSequences and SeriesConvergence of sequencesHard
- 25Continuity and differentiability at zero of a piecewise oscillating functionCalculusDifferential calculus of one variableHard
- 26Limit of a ratio vanishing to third order at one halfCalculusDifferential calculus of one variableHard
- 27Number of distinct eigenvalues of the all-ones matrixMatrices and DeterminantsEigenvalues and eigenvectorsMedium
- 28Limit in probability of the mean of squared deviations of a shifted exponentialLimit TheoremsWeak law of large numbersMedium
- 29UMVUE of the parameter of a double exponential densityEstimationUMVUEHard
- 30Variance of a variable from a wedge-shaped joint densityMultivariate DistributionsConditional distributionsHard
- 31Sample size from Chebyshev's inequality for a proportion of headsLimit TheoremsChebyshev and Markov inequalitiesMedium
- 32Probability that a random matrix built from two binomial variables is orthogonalDescriptive Statistics and ProbabilityProbabilityHard
- 33MLE of the rate of a Weibull-type densityEstimationMaximum likelihood estimationMedium
- 34Incorrect statement about estimators for a uniform distributionEstimationSufficiency and completenessMedium
- 35Solution of a first-order differential equation by substitutionDifferential EquationsExistence & uniquenessHard