Mathematical Statistics 2012
15 questions, booklet MS2012.
Section A · Section A · Q1–15
Practise this section →- 1Eigenvector of a triangular matrix with a repeated eigenvalueMatrices and DeterminantsEigenvalues and eigenvectorsEasy
- 2Volume of the solid generated by a square-root curveCalculusIntegral calculusEasy
- 3Order of integration reversed for a region between a parabola and a lineCalculusIntegral calculusMedium
- 4Limit of n times a sum of shifted sine valuesSequences and SeriesConvergence of sequencesHard
- 5Continuity and partial derivatives at a point for an oscillating function of two variablesCalculusDifferential calculus of two variablesHard
- 6Divergence of a series with terms tending to a positive limitSequences and SeriesConvergence of seriesEasy
- 7Probability that a random four digit number has exactly two zerosDescriptive Statistics and ProbabilityProbabilityMedium
- 8Probability of destroying a target at a later attemptDescriptive Statistics and ProbabilityProbabilityMedium
- 9Variance of a binomial variable from a pmf ratioUnivariate DistributionsBinomial distributionMedium
- 10Correlation between a sum of two normals and the total of eightMultivariate DistributionsCorrelation and covarianceMedium
- 11Lower quantile of an F distribution from an upper quantile of the reciprocalSampling DistributionsF distributionMedium
- 12Limiting probability that a sum of exponentials exceeds its meanLimit TheoremsCentral Limit Theorem (i.i.d. and finite variance case)Easy
- 13Unbiased estimator of the square of a range parameterEstimationUnbiased estimatorsHard
- 14Sample size from the half-width of a confidence intervalEstimationConfidence intervalsMedium
- 15Type I and Type II errors for a two-sided binomial testTesting of HypothesesType I and Type II errorsMedium