Statistics Paper I 2025
80 questions, booklet ISS-2025-P1.
Section I · Objective (Q1–Q80) · Q1–80
Practise this section →- 1Distribution Theory — mode of Beta first kindDistribution TheoryProbabilityEasy
- 2Distribution Theory — modes of the Beta densityDistribution TheoryProbabilityMedium
- 3Distribution Theory — linear transform of uniform variateDistribution TheoryProbabilityEasy
- 4Probability — expected win from dice and coinProbabilityProbabilityEasy
- 5Probability — expected escape time for trapped minerProbabilityProbabilityMedium
- 6Distribution Theory — cdf of standard Laplace distributionDistribution TheoryProbabilityEasy
- 7Distribution Theory — marginal from triangular joint densityDistribution TheoryProbabilityEasy
- 8Distribution Theory — mean of a quadratic densityDistribution TheoryProbabilityEasy
- 9Distribution Theory — variance from factorised mgfDistribution TheoryProbabilityMedium
- 10Distribution Theory — asymptotic normality of chi-squareDistribution TheoryStatistical MethodsMedium
- 11Probability — independence from a contingency tableProbabilityStatistical MethodsMedium
- 12Distribution Theory — cumulants in terms of raw momentsDistribution TheoryProbabilityEasy
- 13Distribution Theory — conditional moments of bivariate normalDistribution TheoryStatistical MethodsMedium
- 14Multivariate Analysis — first-order partial correlationMultivariate AnalysisStatistical MethodsMedium
- 15Descriptive Statistics — properties of correlation ratioDescriptive StatisticsStatistical MethodsMedium
- 16Probability — covariance from a joint pmf tableProbabilityProbabilityMedium
- 17Distribution Theory — minimum of geometric random variablesDistribution TheoryStatistical MethodsMedium
- 18Distribution Theory — marginal of bivariate normalDistribution TheoryStatistical MethodsEasy
- 19Statistical Inference — smallest significant value of r-squaredStatistical InferenceStatistical Inference and Hypothesis TestingMedium
- 20Descriptive Statistics — association between literacy and criminalityDescriptive StatisticsStatistical MethodsMedium
- 21Numerical Analysis — operator inverse on geometric functionNumerical AnalysisNumerical AnalysisMedium
- 22Numerical Analysis — fifth forward difference of reciprocalNumerical AnalysisNumerical AnalysisMedium
- 23Numerical Analysis — divided difference of reciprocal functionNumerical AnalysisNumerical AnalysisHard
- 24Numerical Analysis — trapezoidal value from Simpson estimateNumerical AnalysisNumerical AnalysisMedium
- 25Numerical Analysis — Simpson's rule area computationNumerical AnalysisNumerical AnalysisMedium
- 26Numerical Analysis — step size from trapezoidal errorNumerical AnalysisNumerical AnalysisMedium
- 27Numerical Analysis — degree of precision of quadrature rulesNumerical AnalysisNumerical AnalysisEasy
- 28Numerical Analysis — error in forward Euler methodNumerical AnalysisNumerical AnalysisMedium
- 29Numerical Analysis — error in first Picard iterateNumerical AnalysisNumerical AnalysisMedium
- 30Numerical Analysis — Euler method over three stepsNumerical AnalysisNumerical AnalysisEasy
- 31Computer Applications — topology using a single backboneComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 32Computer Applications — central device in star topologyComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 33Computer Applications — time-slice based CPU schedulingComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 34Computer Applications — advantages of solid-state storageComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 35Computer Applications — number system conversionsComputer Applications & Data ProcessingComputer application and Data ProcessingMedium
- 36Computer Applications — features of Linux operating systemComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 37Computer Applications — memory requirement of an algorithmComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 38Computer Applications — role of the runtime environmentComputer Applications & Data ProcessingComputer application and Data ProcessingMedium
- 39Computer Applications — purpose of breakpoints in debuggingComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 40Computer Applications — server role in client-server DBMSComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 41Distribution Theory — marginal of a multinomial componentDistribution TheoryProbabilityEasy
- 42Distribution Theory — correlation of multinomial countsDistribution TheoryStatistical MethodsMedium
- 43Distribution Theory — conditional mean in multinomialDistribution TheoryProbabilityMedium
- 44Distribution Theory — conditional variance in multinomialDistribution TheoryProbabilityMedium
- 45Distribution Theory — mean of a compound Poisson variableDistribution TheoryProbabilityHard
- 46Distribution Theory — variance of compound Poisson variableDistribution TheoryProbabilityHard
- 47Distribution Theory — mgf of compound Poisson variableDistribution TheoryProbabilityHard
- 48Distribution Theory — Poisson approximation for rare eventDistribution TheoryProbabilityEasy
- 49Probability — limit of sample mean for shifted exponentialProbabilityStatistical MethodsEasy
- 50Distribution Theory — fourth central moment from characteristic functionDistribution TheoryProbabilityMedium
- 51Probability — asymptotic behaviour of empirical cdfProbabilityProbabilityMedium
- 52Distribution Theory — density of radial distanceDistribution TheoryProbabilityHard
- 53Descriptive Statistics — class frequencies of three attributesDescriptive StatisticsStatistical MethodsHard
- 54Distribution Theory — probability from uniform mean and varianceDistribution TheoryProbabilityMedium
- 55Distribution Theory — normal interval probability using cdfDistribution TheoryProbabilityEasy
- 56Distribution Theory — degrees of freedom under linear restrictionsDistribution TheoryStatistical MethodsMedium
- 57Distribution Theory — scaled minimum of exponential sampleDistribution TheoryStatistical MethodsMedium
- 58Distribution Theory — conditional probability for normal variateDistribution TheoryProbabilityMedium
- 59Distribution Theory — constant making a t-distributed ratioDistribution TheoryStatistical MethodsHard
- 60Descriptive Statistics — Yule's coefficients in a 2x2 tableDescriptive StatisticsStatistical MethodsMedium
- 61Numerical Analysis — function with given first differenceNumerical AnalysisNumerical AnalysisMedium
- 62Numerical Analysis — forward difference second derivativeNumerical AnalysisNumerical AnalysisEasy
- 63Numerical Analysis — inverse of Lagrange interpolation polynomialNumerical AnalysisNumerical AnalysisMedium
- 64Numerical Analysis — Lagrange interpolation of composed functionNumerical AnalysisNumerical AnalysisHard
- 65Numerical Analysis — Picard iterate at the initial pointNumerical AnalysisNumerical AnalysisEasy
- 66Numerical Analysis — forward and backward operator identitiesNumerical AnalysisNumerical AnalysisMedium
- 67Numerical Analysis — hundredth difference of a monomialNumerical AnalysisNumerical AnalysisMedium
- 68Numerical Analysis — central difference second derivative valueNumerical AnalysisNumerical AnalysisMedium
- 69Numerical Analysis — two-point rule of maximum precisionNumerical AnalysisNumerical AnalysisHard
- 70Numerical Analysis — Lagrange interpolation at four nodesNumerical AnalysisNumerical AnalysisMedium
- 71Computer Applications — role of flowcharts in problem solvingComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 72Computer Applications — purpose of the linker in compilationComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 73Computer Applications — characteristics of virtual realityComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 74Computer Applications — components of multimediaComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 75Computer Applications — working of a network routerComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 76Computer Applications — repeated execution control structureComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 77Computer Applications — purpose of virtual memoryComputer Applications & Data ProcessingComputer application and Data ProcessingMedium
- 78Computer Applications — function of a packet filter firewallComputer Applications & Data ProcessingComputer application and Data ProcessingMedium
- 79Computer Applications — IEEE standard behind Wi-FiComputer Applications & Data ProcessingComputer application and Data ProcessingEasy
- 80Computer Applications — unit performing AND and ORComputer Applications & Data ProcessingComputer application and Data ProcessingEasy