Indian Statistical Service Examination (with Indian Economic Service)
India · Union Public Service Commission · civil-service · unverified source
851practice questions written to this syllabus
35subjects
Format
Written examination of six papers and a viva voce. Reported scheme: General English 100, General Studies 100, Statistics I and II (objective, 200 each), Statistics III and IV (descriptive, 200 each); viva 200.
Statistics II: linear models, estimation, hypothesis testing, multivariate analysis
Statistics III: sampling techniques, design of experiments, economic statistics, SQC and operations research (reported)
Statistics IV: optional areas such as stochastic processes, demography and vital statistics, computing, time series and econometrics (reported)
General English; General Studies
Over the years
Built from Laisha's knowledge because the official page could not be opened or was not found during research (web search quota exhausted); confirm against the body's current notification before relying on it. upsc.gov.in returned 403 to Laisha's fetcher. ISS officers staff MoSPI, the National Statistical Office and statistics divisions of ministries including agriculture. Paper contents are as Laisha knows them and are marked 'reported' in curriculum weights.
Original questions written to this exam's published syllabus and pattern. Not past papers.
1. In the logistic model dN/dt = rN(1 − N/K) with K = 1,000, population growth is fastest when N equals:
500
1,000
368
250
Answer and working
A. 500
The inflection is at K/2. 368 ≈ K/e is the Gompertz inflection.
Differential Equations, Finite Differences & Numerical Analysis · Ordinary differential equations of first order: exact, linear and Bernoulli equations
2. Grain yields from a field contain a mixture of plots sown with two varieties that differ by about 1.5 t/ha. What shape is the frequency curve of all plot yields most likely to show?
J-shaped, with the highest frequency at the lowest yield
U-shaped, with the lowest frequency in the middle classes only because of measurement error
Bimodal, with two humps
Symmetrical and mesokurtic like a single normal curve
Answer and working
C. Bimodal, with two humps
A mixture of two populations whose means differ by much more than their spread gives two peaks. A J-shape is typical of counts with many zeros; a single symmetrical curve would hide the mixture only if the means were close.
Statistical Methods for Agricultural Sciences · Statistics: definition, uses and limitations; frequency distributions and curves
3. Let A be an event with ∅ ≠ A ≠ Ω. What is the smallest σ-field on Ω that contains A?
{∅, A, Ω}
The power set of Ω
{A, Aᶜ}
{∅, A, Aᶜ, Ω}
Answer and working
D. {∅, A, Aᶜ, Ω}
Any σ-field containing A must contain Aᶜ (complements) and Ω and ∅. The collection {∅, A, Aᶜ, Ω} already satisfies all three conditions, so it is the smallest. {∅, A, Ω} lacks Aᶜ; {A, Aᶜ} lacks Ω; the power set contains A but is generally far larger than necessary.
Probability Theory · Sample spaces, sigma-fields and the axioms of probability
4. X is binomial with n = 9 and p = 0.4. What is the mode of X?
4 only
3.6, the mean
Both 3 and 4, with equal probability
3 only
Answer and working
C. Both 3 and 4, with equal probability
(n + 1)p = 10 × 0.4 = 4 is an integer, so P(X = 3) = P(X = 4) and both are modes: P(3) = 0.2508, P(4) = 0.2508. The mean np = 3.6 is not even a possible value.
Probability Distributions & Sampling Distributions · Discrete distributions: Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric and multinomial
5. The number of insects on a plant, recorded continuously through a day, is which type of stochastic process?
Continuous time, continuous state
Continuous time, discrete state
Discrete time, continuous state
Discrete time, discrete state
Answer and working
B. Continuous time, discrete state
Time runs continuously and the count takes values 0, 1, 2, .... Daily wet/dry records would be discrete time and discrete state.
Stochastic Processes · Definition and classification of stochastic processes
Practise it, and prove it
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