China national postgraduate entrance exam - Statistics (0714) and Applied Statistics master's (432)

China · Ministry of Education / China Higher Education Student Information (CHSI) with universities · pg · unverified source

183practice questions written to this syllabus
13subjects

Format

National unified exam: politics, English, mathematics (for academic statistics) and a specialised paper; applied-statistics master's uses the 432 Statistics paper (reported).

Sections

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. Agricultural universities (e.g. China Agricultural University) admit to statistics and biostatistics programmes through this route.

Official source: https://yz.chsi.com.cn/

Subjects this exam draws on

Real Analysis for Statistics2 questionsLinear Algebra & Matrix Theory for Statistics3 questionsProbability Theory13 questionsProbability Distributions & Sampling Distributions14 questionsStochastic Processes76 questionsStatistical Inference I: Estimation19 questionsStatistical Inference II: Testing of Hypotheses & Sequential Analysis9 questionsNonparametric & Rank-Based Methods9 questionsMultivariate Analysis14 questionsBayesian Inference13 questionsBioassay, Survival & Epidemiological Statistics1 questionsOptimization Techniques for Statisticians9 questionsStatistical Quality Control & Reliability1 questions

Five practice questions, worked

Original questions written to this exam's published syllabus and pattern. Not past papers.

1. What is lim n³/2ⁿ as n → ∞?

  1. 0
  2. ∞
  3. 1
  4. 3/2
Answer and working

A. 0

Exponentials with base greater than 1 dominate any power of n.

Real Analysis for Statistics · Sequences: convergence, monotone and Cauchy sequences

2. The inverse of an orthogonal matrix Q is:

  1. −Q
  2. Q²
  3. Q′
  4. I − Q
Answer and working

C. Q′

Q′Q = I, so Q⁻¹ = Q′ (the transpose).

Linear Algebra & Matrix Theory for Statistics · Determinants, inverses and partitioned matrices

3. A seed lot is 'good' with prior probability 0.9 and 'poor' otherwise. Seeds from a good lot germinate independently with probability 0.9, from a poor lot with probability 0.5. Two seeds are tested and both germinate. What is the posterior probability that the lot is good?

  1. 0.7290
  2. 0.9419
  3. 0.9668
  4. 0.9000
Answer and working

C. 0.9668

Likelihoods: good 0.9² = 0.81, poor 0.5² = 0.25. Posterior = 0.9 × 0.81/(0.9 × 0.81 + 0.1 × 0.25) = 0.729/0.754 = 0.9668. 0.9419 uses only one seed; 0.7290 is the joint probability, not divided by P(both germinate).

Probability Theory · Conditional probability, independence and Bayes' theorem

4. X and Y are independent Poisson variables with means 2 and 3. What is P(X = 2 | X + Y = 4)?

  1. 0.3750
  2. 0.4000
  3. 0.3456
  4. 0.2707
Answer and working

C. 0.3456

Given X + Y = 4, X ~ binomial(4, 2/5): P(X = 2) = C(4, 2)(0.4)²(0.6)² = 0.3456. 0.2707 is the unconditional P(X = 2); 0.3750 uses p = 1/2, ignoring the unequal means.

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?

  1. Continuous time, continuous state
  2. Continuous time, discrete state
  3. Discrete time, continuous state
  4. 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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