Mathematical Statistics 2022
60 questions, booklet MS2022.
Section A · Section A · Q1–30
Practise this section →- 1Contractive sequence is CauchySequences and SeriesSequences and Series of real numbersEasy
- 2Derivative of x sin of reciprocalCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 3Maximum of a parameterized determinantMatrices and DeterminantsMatrices and DeterminantsMedium
- 4Dependence and conditional probabilityDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 5Validity of a moment generating functionUnivariate DistributionsUnivariate DistributionsEasy
- 6Expectation of reciprocal binomialUnivariate DistributionsUnivariate DistributionsEasy
- 7Expected value in a bivariate densityMultivariate DistributionsMultivariate DistributionsEasy
- 8Minimum of two geometric variablesUnivariate DistributionsUnivariate DistributionsEasy
- 9UMVUE for exponential distributionEstimationEstimationMedium
- 10Simple null hypothesis in normal distributionTesting of HypothesesTesting of HypothesesEasy
- 11Limit of a Riemann sumCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 12Differentiability of bivariate functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 13Arc length of an integral functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 14Derivative of integral with floor functionCalculusDifferential Calculus of one and two real variables, and Integral CalculusHard
- 15Linear system with infinite solutionsMatrices and DeterminantsMatrices and DeterminantsMedium
- 16Sum of elements of matrix powerMatrices and DeterminantsMatrices and DeterminantsMedium
- 17Elevator exit floor probabilityDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityHard
- 18Conditional probability of leap FebruaryDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityHard
- 19Waiting time for head followed by tailStochastic ProcessesStochastic ProcessesMedium
- 20Probability bounds for gamma variableLimit TheoremsStochastic ProcessesEasy
- 21Optimal inventory under exponential demandUnivariate DistributionsUnivariate DistributionsMedium
- 22Expectation of log uniform ratioMultivariate DistributionsMultivariate DistributionsMedium
- 23Conditional probability in bivariate normalMultivariate DistributionsMultivariate DistributionsMedium
- 24Limit in probability for Pareto sampleLimit TheoremsLimit TheoremsEasy
- 25MLE and MOM for piecewise uniformEstimationEstimationMedium
- 26Properties of Student t statisticSampling DistributionsSampling DistributionsMedium
- 27Order statistics from uniform sampleSampling DistributionsSampling DistributionsMedium
- 28Confidence interval for normal meanEstimationEstimationHard
- 29Non-existence of certain test sizeTesting of HypothesesTesting of HypothesesMedium
- 30Power of Poisson likelihood ratio testTesting of HypothesesTesting of HypothesesMedium
Section B · Section B · Q31–40
Practise this section →- 31Convergence of reciprocal seriesSequences and SeriesSequences and Series of real numbersHard
- 32Critical points of bivariate polynomialCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 33Properties of orthogonal and skew-symmetric matricesMatrices and DeterminantsMatrices and DeterminantsHard
- 34Properties of countable probability spacesDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityHard
- 35Distribution of capped insurance payoutUnivariate DistributionsUnivariate DistributionsMedium
- 36Independence and distribution of normal sumsMultivariate DistributionsMultivariate DistributionsMedium
- 37Properties of discrete random vectorsDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 38Distribution of normal variance ratiosSampling DistributionsSampling DistributionsHard
- 39MLE and sufficiency for Laplace locationEstimationEstimationHard
- 40Power function of normal mean testTesting of HypothesesTesting of HypothesesMedium
Section C · Section C · Q41–60
Practise this section →- 41Limit superior and inferior of periodic sequenceSequences and SeriesSequences and Series of real numbersEasy
- 42Determining function from two-sided boundsCalculusDifferential Calculus of one and two real variables, and Integral CalculusEasy
- 43Trace of matrix from its adjointMatrices and DeterminantsMatrices and DeterminantsMedium
- 44Probability between power and linear boundsMultivariate DistributionsMultivariate DistributionsEasy
- 45Expected runs in Bernoulli trialsDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityEasy
- 46Variance of scaled insurance paymentUnivariate DistributionsUnivariate DistributionsEasy
- 47Probability of absolute sum of discrete variablesMultivariate DistributionsMultivariate DistributionsEasy
- 48Tail probability of chi-square sumSampling DistributionsSampling DistributionsMedium
- 49Method of moments for Laplace-normal mixtureEstimationEstimationMedium
- 50Type-II error probability in normal testTesting of HypothesesTesting of HypothesesMedium
- 51Extrema on a circleCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 52Double integral with variable substitutionCalculusDifferential Calculus of one and two real variables, and Integral CalculusMedium
- 53Unit eigenvector of symmetric matrixMatrices and DeterminantsMatrices and DeterminantsHard
- 54Exactly one match in restaurant ordersDescriptive Statistics and ProbabilityDescriptive Statistics and ProbabilityMedium
- 55Expectation of quadratic polynomial densityUnivariate DistributionsUnivariate DistributionsMedium
- 56Coefficient of variation of binomial sumSampling DistributionsSampling DistributionsEasy
- 57Median of limiting scaled minimumLimit TheoremsLimit TheoremsMedium
- 58Finite moments of Pareto order statisticsSampling DistributionsSampling DistributionsHard
- 59Sum of least squares regression estimatesEstimationEstimationMedium
- 60P-value of one-sided t-testTesting of HypothesesTesting of HypothesesMedium