GATE Statistical Computing: Simulation, Resampling & Algorithms: practice questions

GATE - Data Science and Artificial Intelligence (DA) · India · IITs and IISc on rotation (2026: IIT Guwahati)

Original practice questions written to the published syllabus · not past papers

6worked here, free

20written to this exam in this subject

11syllabus units

What this subject covers

The algorithms inside modern statistics: random-number generation, Monte Carlo integration, the bootstrap and jackknife, permutation tests, the EM algorithm, MCMC and numerical linear algebra, with attention to accuracy and reproducibility.

In the exams: AICE-JRF Computer Application Unit 10 (present); GATE DA (present); PhD course in most programmes; light in national exams

Pseudo-random number generation and tests of randomness
Generating random variates: inversion, acceptance-rejection and transformation methods
Monte Carlo integration and variance reduction
Bootstrap: percentile and BCa intervals
Jackknife
Permutation and randomisation tests
EM algorithm and its applications (missing data, mixtures)
MCMC algorithms in practice
Numerical linear algebra for statistics: QR and Cholesky
Simulation studies: design and reporting
Parallel and high-performance computing for statistics

Where the 20 questions fall

How our questions for GATE spread across the units of Statistical Computing: Simulation, Resampling & Algorithms. Difficulty: 10 easy, 10 medium, 0 hard.

Pseudo-random number generation and tests of randomness	3
Generating random variates: inversion, acceptance-rejection and transformation methods	2
Monte Carlo integration and variance reduction	2
Bootstrap: percentile and BCa intervals	2
Jackknife	2
Permutation and randomisation tests	2
MCMC algorithms in practice	2
Parallel and high-performance computing for statistics	2
EM algorithm and its applications (missing data, mixtures)	1
Numerical linear algebra for statistics: QR and Cholesky	1
Simulation studies: design and reporting	1

6 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Pseudo-random number generation and tests of randomness · easy

For the generator xₙ₊₁ = (5xₙ + 3) mod 16 with x₀ = 7, what is x₁?

Answer and working

B. 6

5 × 7 + 3 = 38, and 38 mod 16 = 6; 38 forgets the modulus.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

2 · Generating random variates: inversion, acceptance-rejection and transformation methods · medium

The inversion method generates X from distribution F as:

F⁻¹(U), with U uniform on (0, 1)
F(U), with U uniform on (0, 1)
U/F(U)
1 − F(U)²

Answer and working

A. F⁻¹(U), with U uniform on (0, 1)

The probability integral transform runs in reverse.

3 · Generating random variates: inversion, acceptance-rejection and transformation methods · easy

To generate a Bernoulli(p) variable from U uniform on (0, 1), return 1 if:

U > p²
U = p
U < p
U < 1 − p²

Answer and working

C. U < p

P(U < p) = p for a uniform U, so the result is 1 with probability p.

4 · Bootstrap: percentile and BCa intervals · medium

A 95% percentile bootstrap interval uses:

θ̂ ± 1.96 times the data SD
The minimum and maximum of θ̂*
The 5th and 95th percentiles
The 2.5th and 97.5th percentiles of θ̂*

Answer and working

D. The 2.5th and 97.5th percentiles of θ̂*

The normal-theory interval would use the bootstrap SE instead.

5 · Permutation and randomisation tests · easy

How many distinct ways are there to assign 10 observations into two groups of 5?

100
3,628,800
32
252

Answer and working

D. 252

C(10, 5) = 252; 3,628,800 is 10!.

6 · Parallel and high-performance computing for statistics · easy

Bootstrap resamples and simulation replicates are called 'embarrassingly parallel' because they:

Tasks are independent
They cannot be parallelised on any hardware
Must run in strict sequence
Need one shared random number

Answer and working

A. Tasks are independent

Each worker can run its own share.

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