Competitive Stats

Limit Theorems

45 questions across 9 topics.

Practise Limit Theorems Filter in the bank

Limit Theorems

Central Limit Theorem (i.i.d. and finite variance case)

38Sequences converging to a normal with mean zeroIIT JAM 2019 MSCentral Limit Theorem (i.i.d. and finite variance case)Medium
21Limit of chi-square tail probabilitiesIIT JAM 2018 MSCentral Limit Theorem (i.i.d. and finite variance case)Hard
59Variance from a central limit approximationIIT JAM 2017 MSCentral Limit Theorem (i.i.d. and finite variance case)Medium
12Asymptotic standard deviation of the mean of oddsIIT JAM 2016 MSCentral Limit Theorem (i.i.d. and finite variance case)Hard
45Normal approximation to a binomial probabilityIIT JAM 2016 MSCentral Limit Theorem (i.i.d. and finite variance case)Medium
55Normal approximation for a sum of gamma variablesIIT JAM 2016 MSCentral Limit Theorem (i.i.d. and finite variance case)Medium
39Limit theorems for i.i.d. variables with given mean and varianceIIT JAM 2015 MSCentral Limit Theorem (i.i.d. and finite variance case)Medium
53Limit of a sum of uniforms with an n to the three quarters thresholdIIT JAM 2015 MSCentral Limit Theorem (i.i.d. and finite variance case)Hard
18Limit of a probability for a sum of uniform variablesIIT JAM 2014 MSCentral Limit Theorem (i.i.d. and finite variance case)Medium
6Limit distribution of a normalised sum of differences of pairsIIT JAM 2013 MSCentral Limit Theorem (i.i.d. and finite variance case)Medium
12Limiting probability that a sum of exponentials exceeds its meanIIT JAM 2012 MSCentral Limit Theorem (i.i.d. and finite variance case)Easy

Weak law of large numbers

Convergence in distribution

Estimation

44Constant in a paired-difference variance estimatorIIT JAM 2025 MSEstimationEasy

Stochastic Processes

20Probability bounds for gamma variableIIT JAM 2022 MSStochastic ProcessesEasy

Asymptotic distributions

14Limit of the normalised maximum of exponential variablesIIT JAM 2016 MSAsymptotic distributionsHard

Poisson approximation

20Probability that a biscuit has no cashew nutsIIT JAM 2015 MSPoisson approximationMedium

Chebyshev and Markov inequalities

31Sample size from Chebyshev's inequality for a proportion of headsIIT JAM 2014 MSChebyshev and Markov inequalitiesMedium