PTS2 — Exam Intelligence Report
PROBABILITY & STATISTICSQUANTITATIVE6 PAPERS ANALYSED
12Study Nodes
6Papers
15HL Questions
100~Marks/Paper
Course CoreProbability Theory and Statistics 2 at the UvA tests quantitative reasoning through six exam types spanning distributions, transformations, CIs, and hypothesis testing. The exam rewards genuine understanding over memorisation.
Top cluster: Hypothesis Testing and Bivariate Distributions both score 10/10 leverage — together representing 40–50% of total marks.
Priority Topic Ranking
| Rank | Topic | Appearances | Avg Marks | Leverage | Level |
|---|---|---|---|---|---|
| #1 | Hypothesis Testing | 6of 6 | 16 | 10 | High |
| #2 | Bivariate Distributions | 6of 6 | 20 | 10 | High |
| #3 | Confidence Intervals | 6of 6 | 8 | 9 | High |
| #4 | Power of a Test | 5of 6 | 4 | 8 | Medium |
| #5 | Transformations | 5of 6 | 9 | 8 | Medium |
| #6 | Sampling Distributions | 5of 6 | 6 | 8 | Medium |
| #7 | Two-Sample Inference | 4of 6 | 8 | 8 | Medium |
| #8 | Marginal & Conditional | 4of 6 | 6 | 7 | Medium |
| #9 | Order Statistics | 4of 6 | 6 | 7 | Medium |
| #10 | p-value Calculation | 4of 6 | 4 | 7 | Medium |
| #11 | Estimation (MLE/MOM) | 3of 6 | 7 | 6 | Low |
| #12 | Covariance | 4of 6 | 4 | 6 | Low |
Key insight: Mastering Hypothesis Testing + Bivariate Distributions alone covers 40-50% of marks.
Core Technical Skills
| Skill | Topics | Level |
|---|---|---|
| Construct & verify joint pmf/pdf | Bivariate | Application |
| Calculate marginals via integration | Bivariate | Analysis |
| Derive conditional PDFs | Conditional | Analysis |
| Compute Cov & Corr | Covariance | Application |
| Test independence | Bivariate | Application |
| Normalise over non-rect. support | Transformations | Analysis |
| CDF method for Z=g(X,Y) | Transformations | Analysis |
| Jacobian change-of-variables | Transformations | Analysis |
| Derive order statistic PDF | Order Stats | Analysis |
| Construct chi-squared/t/F | Sampling | Analysis |
| MLE by log-likelihood | Estimation | Analysis |
| CI for mean (z and t) | CI | Application |
| CI for variance ratio (F) | CI | Analysis |
| 6-step hypothesis test | Hyp Testing | Synthesis |
| Compute power | Power | Analysis |
| Two-proportion test | Hyp Testing | Analysis |
Highest-leverage skill: The 6-step hypothesis test protocol — required for nearly every question in the inference section. It synthesises skills from every prior node.
Final vs. Resit Exam Patterns
Final Exam
- 3-4 questions, ~100 marks, 2.5-3 hours
- Q1 is always the large bivariate question (18-21 marks)
- Q2 is typically transformations (CDF or Jacobian)
- Q3/Q4 rotate among CIs, hypothesis testing, sampling distributions
- Non-rectangular supports common — the most costly error
Resit Exam
- Often same structure as finals
- Some resits identical to the final (2025)
- Hypothesis Testing explicitly demands "all 6 steps"
- Two-sample inference is a recurrent archetype
Trap awareness: "From scratch" in Order Statistics means derive from CDF, no formula quoting. "Hence" means use the previous part's result. "State the distribution" requires full justification.
Multi-Part Scaffolds
Canonical Progression
- (a) Foundational setup — construct pmf/pdf, find c, draw support. 2-5 marks.
- (b) First computation — marginals, probability, simple interval. 3-6 marks.
- (c) Extended computation — full transformation, conditional, power. 4-8 marks.
- (d)/(e) Synthesis — "from scratch" derivation, context interpretation. 2-5 marks.
Partial credit flows upward: Errors in (a) that carry into (b) earn follow-through marks. Wrong method earns zero regardless of arithmetic.
Node Progression (12 Nodes)
Nodes ordered by prerequisite dependency.
1Foundations of Bivariate DistributionsLev: 9/10
2Conditional, Independence & CovarianceLev: 9/10
3Non-Rectangular Supports & IntegrationLev: 9/10
4TransformationsLev: 8/10
5Order StatisticsLev: 7/10
6Sampling DistributionsLev: 8/10
7Point EstimationLev: 6/10
8CI: One-SampleLev: 9/10
9CI: Two-SampleLev: 8/10
10Hypothesis TestingLev: 10/10
11Power of a TestLev: 8/10
12Two-Sample TestsLev: 9/10
N1 → N2 → N3 → N4 → N5
↓
N6 → N7 → N8 → N9 → N10 → N11 → N12
Priority for limited time: Focus on N1-N3 (bivariate), N10 (hypothesis testing), N8-N9 (CIs), N11-N12 (power, two-sample). These cover 75%+ of marks.
Practice Menu (15 Questions)
| # | Source | Topic | Marks | Difficulty |
|---|---|---|---|---|
| HLQ 1 | final_2023 Q1 | Bivariate | 8 | Core |
| HLQ 2 | final_2023 Q1(c-d) | Covariance + Continuous | 11 | Distinction |
| HLQ 3 | final_2023 Q2 | Transformations | 10 | Distinction |
| HLQ 4 | final_2024 Q2 | Order Statistics | 5 | Distinction |
| HLQ 5 | final_2024 Q3 | Sampling Distributions | 5 | Core |
| HLQ 6 | final_2024 Q4 | CI Two-Sample | 9 | Core |
| HLQ 7 | final_2024 Q5 | Hypothesis Testing | 12 | High |
| HLQ 8 | final_2025 Q1 | Bivariate Discrete | 11 | Core |
| HLQ 9 | final_2025 Q1(d-e) | Bivariate Continuous | 8 | Distinction |
| HLQ 10 | final_2025 Q2 | Transformations CDF | 6 | Distinction |
| HLQ 11 | resit_2025 Q5 | CI Variance Ratio | 7 | Core |
| HLQ 12 | resit_2025 Q7(b) | Two Proportions | 7 | High |
| HLQ 13 | final_2025 Q3 | Two-Sample Means | 18 | High |
| HLQ 14 | resit_2024 Q3 | z/t/p-value | 10 | High |
| HLQ 15 | final_2023 Q3 | Sampling Distributions | 7 | Core |
Exam Day Strategy
- First 3 min: Scan all questions. Budget 20% for bivariate (Q1), 25% for inference.
- Bivariate first: Sketch support before integrating. Correct sketch = partial credit.
- Hypothesis testing: Write ALL 6 steps visibly. Correct structure earns 3-4/6 even if calcs wrong.
- Non-rectangular supports: Integration limits must be functions of outer variable, not constants.
- Power: Reuse rejection region from hypothesis test. Power = P(reject | H₁).
- From scratch: Derive CDF first, then differentiate. No formulas.