Mathematical Statistics 2013
18 questions, booklet MS2013.
Section A · Section A · Q1–10
Practise this section →- 1Conditional probability of F given E union F complementDescriptive Statistics and ProbabilityProbabilityMedium
- 2Limit of an expression in a sequence with small ratioSequences and SeriesConvergence of sequencesMedium
- 3Function recovered from a given arc lengthCalculusIntegral calculusHard
- 4Value making a function of two variables continuous at the originCalculusDifferential calculus of two variablesMedium
- 5Trace of the sum of the inverse and the square of a matrixMatrices and DeterminantsEigenvalues and eigenvectorsMedium
- 6Limit distribution of a normalised sum of differences of pairsLimit TheoremsCentral Limit Theorem (i.i.d. and finite variance case)Medium
- 7Distribution of a studentised single observationSampling Distributionst distributionMedium
- 8Bias and consistency of a combination of a sample mean and one new observationEstimationConsistency of estimatorsHard
- 9Critical value of the most powerful test for the rate of a gamma densityTesting of HypothesesMost powerful testsHard
- 10Sign of the mean of a skew-normal densityUnivariate DistributionsMathematical expectation and momentsHard
Section B · Section B · Q12–19
Practise this section →- 12Normalising constant for a joint density on a wedgeMultivariate DistributionsJoint densitiesMedium
- 13Power of a most powerful test with a stated sizeTesting of HypothesesMost powerful testsHard
- 14Posterior probability of a factory given a long bulb lifetimeDescriptive Statistics and ProbabilityBayes theoremMedium
- 15Confidence coefficient of an interval based on the sample minimumEstimationConfidence intervalsMedium
- 16Probability that all bolts in four boxes are goodDescriptive Statistics and ProbabilityProbabilityEasy
- 17Condition for differentiability at a point of a split rational irrational functionCalculusDifferential calculus of one variableHard
- 18Limit involving a bounded sequence and a sine termSequences and SeriesConvergence of sequencesMedium
- 19Condition on parameters for a linear system to be always solvableMatrices and DeterminantsSystems of linear equationsHard