Homework Alignment Analysis
HW vs Schedule Topics
EE 364 Homework Alignment Analysis
Comparison of existing homework assignments against the 15-week schedule.
Schedule Reference
| Week | Topic |
|---|---|
| 1 | Introduction to probability. Logic and sets. Probability axioms. |
| 2 | Independence. Conditional probability. Bayes’ Theorem. |
| 3 | Combinatorics. Binomial and multinomial probability. |
| 4 | Discrete probability and mass functions. Poisson Theorem. |
| 5 | Continuous probability densities. |
| 6 | Expectation, variance. Transformed random variables. |
| 7 | Multiple random variables. Covariance and correlation. Uncertainty principles. |
| 8 | Multivariate normal. Mixtures. Laws of large numbers. |
| 9 | Bayesian statistics and conjugacy. |
| 10 | Maximum likelihood estimation. Entropy. Monte Carlo sampling. |
| 11 | Transforms. Sample mean and sample variance. Central limit theorem. |
| 12 | Confidence intervals. Statistical hypothesis testing. |
| 13 | Optimal estimation and least squares. |
| 14 | Linear regression and multivariable regression. |
| 15 | Logistic Regression. Probability structure of neural classifiers. Review. |
HW 01 Analysis
Assigned: Week 1 | Due: Week 2 | Problems: 0-7 (8 total)
| Problem | Topic | Aligns With |
|---|---|---|
| 0 | Daily derivation: Addition theorem | Week 1 |
| 1 | Truth tables, propositional logic | Week 1 |
| 2 | Set subset proofs | Week 1 |
| 3 | Set theory proofs (De Morgan) | Week 1 |
| 4 | Sample space, subsets | Week 1 |
| 5 | Power sets, cardinality | Week 1 |
| 6 | Sample space, probability measure | Week 1 |
| 7 | Probability bounds on intersections | Week 1 |
Verdict: EXCELLENT - All problems align with Week 1. No forward bleed.
HW 02 Analysis
Assigned: Week 2 | Due: Week 3 | Problems: 0-14 (15 total)
| Problem | Topic | Aligns With |
|---|---|---|
| 0 | Daily derivation: Total Probability, Bayes | Week 2 |
| 1 | Sigma algebras | Week 1-2 |
| 2 | Mathematical induction | Background |
| 3 | Epsilon-delta limits | Background |
| 4 | Integration by parts | Background |
| 5 | Independence | Week 2 |
| 6 | Independence of events | Week 2 |
| 7 | Conditional probability | Week 2 |
| 8 | Bayes’ theorem (posterior) | Week 2 |
| 9 | Conditional probability proof | Week 2 |
| 10-14 | Bayes’ theorem applications | Week 2 |
Verdict: GOOD - Core problems align with Week 2. Problems 2-4 are mathematical background (limits, integration). Heavy on Bayes applications.
HW 03 Analysis
Assigned: Week 3 | Due: Week 4 | Problems: 0-14 (15 total)
| Problem | Topic | Aligns With |
|---|---|---|
| 0 | Daily derivation: Binomial Theorem | Week 3 |
| 1 | Combinations | Week 3 |
| 2 | Multinomial probability | Week 3 |
| 3 | Counting (shoes) | Week 3 |
| 4 | Derangements | Week 3 |
| 5 | Permutations | Week 3 |
| 6 | Binomial identity | Week 3 |
| 7 | Binomial probability | Week 3 |
| 8 | Bayesian inference with dice | Week 2/9 |
| 9 | Binomial (coin flipping) | Week 3 |
| 10 | Hypergeometric | Week 4 |
| 11 | Hypergeometric | Week 4 |
| 12 | Conditional + hypergeometric | Week 2/4 |
| 13 | Hypergeometric | Week 4 |
| 14 | Mixture distributions | Week 8 |
Verdict: BLEEDS FORWARD - Problems 10-13: Hypergeometric → Week 4 - Problem 14: Mixtures → Week 8 - Problem 8: Bayesian updating → Week 9
HW 04 Analysis
Assigned: Week 4 | Due: Week 5 | Problems: 0-16 (17 total)
| Problem | Topic | Aligns With |
|---|---|---|
| 0 | Daily derivation: Poisson Law | Week 4 |
| 1 | Inverse image sets | Week 1 (sets) |
| 2-3 | Series convergence tests | Background |
| 4 | Proof by contradiction | Background |
| 5 | Negative binomial | Week 4 |
| 6 | Geometric distribution | Week 4 |
| 7-8 | Poisson distribution | Week 4 |
| 9 | Order statistics (min/max) | Week 7 |
| 10 | Hazard rate, PMF, CDF | Week 4/5 |
| 11 | Bayesian model selection | Week 9/10 |
| 12 | Binomial | Week 3/4 |
| 13 | Binomial | Week 3/4 |
| 14 | Negative binomial | Week 4 |
| 15 | Geometric series | Week 4 |
| 16 | PGF (generating functions) | Week 11 |
Verdict: BLEEDS FORWARD - Problem 9: Order statistics → Week 7 - Problem 11: Bayesian model selection → Week 9/10 - Problem 16: Generating functions → Week 11
HW 05 Analysis
Assigned: Week 5 | Due: Week 6 | Problems: 0-20 (21 total)
| Problem | Topic | Aligns With |
|---|---|---|
| 0 | Daily derivation: Beta-Binomial conjugacy | Week 9 |
| 1-2 | Continuous probability | Week 5 |
| 3-5 | PDF/CDF calculations | Week 5 |
| 6 | Expected value (uniform) | Week 6 |
| 7-9 | Uniform distribution | Week 5 |
| 10 | Weibull distribution | Week 5 |
| 11-13 | Gaussian distribution | Week 5 |
| 14 | Signal detection / Bayes | Week 5/12 |
| 15 | Gaussian comparison | Week 5 |
| 16 | FWHM of Gaussian | Week 5/6 |
| 17 | Type I/II errors, thresholds | Week 12 |
| 18 | Conditional probability | Week 2 |
| 19 | Order statistics (min/max CDF) | Week 7 |
| 20 | Mixture conjugate priors | Week 8/9 |
Verdict: SIGNIFICANT BLEED - Problem 0: Conjugacy → Week 9 - Problem 6: Expectation → Week 6 - Problem 14, 17: Hypothesis testing → Week 12 - Problem 19: Order statistics → Week 7 - Problem 20: Mixtures/conjugacy → Week 8/9
HW 06 Analysis
Assigned: Week 6 | Due: Week 7 | Problems: 0-16 (17 total)
| Problem | Topic | Aligns With |
|---|---|---|
| 0 | Daily derivation: All distribution moments | Week 6 (heavy) |
| 1 | Indicator functions | Week 6 |
| 2-5 | Mean and variance calculations | Week 6 |
| 6 | Mixed distribution moments | Week 6/8 |
| 7 | Expected value (independence) | Week 6/7 |
| 8-9 | Gaussian moments | Week 6 |
| 10 | Tail probability integral | Week 6 |
| 11 | Iterated Gaussian | Week 7/8 |
| 12 | Pareto moments | Week 6 |
| 13 | Poisson moments | Week 6 |
| 14 | Moment constraints | Week 6 |
| 15-16 | Transformed RV (limiter) | Week 6 |
Verdict: MOSTLY ALIGNED - Core Week 6 content. Some problems touch Week 7/8 (multiple RVs).
HW 07 Analysis
Assigned: Week 7 | Due: Week 8 | Problems: 0-18 (19 total)
| Problem | Topic | Aligns With |
|---|---|---|
| 0 | Daily derivation: WLLN, sample variance | Week 8/11 |
| 1-4 | Transformed RV pdfs | Week 6 |
| 5-6 | Chebyshev inequality | Week 8 |
| 7-8 | Chebyshev bounds | Week 8 |
| 9-12 | Stochastic convergence | Week 8 |
| 13-15 | Consistent estimators | Week 8/10 |
| 16 | Convergence (probability, mean-square) | Week 8 |
| 17 | Sample variance derivation | Week 11 |
| 18 | Monte Carlo integration | Week 10 |
Verdict: SIGNIFICANT MISALIGNMENT - Schedule Week 7: Multiple RVs, covariance, correlation - HW 07 covers: Convergence (Week 8), transforms (Week 6), Monte Carlo (Week 10) - Missing from HW 07: Covariance, correlation, joint distributions
Summary Table
| HW | Assigned | Aligned? | Forward Bleed | Notes |
|---|---|---|---|---|
| 01 | Week 1 | YES | None | Safe for 1-week |
| 02 | Week 2 | YES | Minor (background math) | Safe for 1-week |
| 03 | Week 3 | PARTIAL | Week 4, 8, 9 | Problems 10-14 bleed |
| 04 | Week 4 | PARTIAL | Week 7, 9, 10, 11 | Scattered bleed |
| 05 | Week 5 | NO | Week 6, 7, 8, 9, 12 | Heavy bleed |
| 06 | Week 6 | YES | Minor (Week 7/8) | Mostly safe |
| 07 | Week 7 | NO | Week 8, 10, 11 | Wrong topic coverage |
Missing Homework Coverage
Topics in schedule with NO homework coverage:
| Week | Topic | HW Coverage |
|---|---|---|
| 7 | Multiple RVs, covariance, correlation | MISSING |
| 8 | Multivariate normal, mixtures | MISSING (partial in HW 05, 07) |
| 9 | Bayesian statistics, conjugacy | Scattered (HW 03, 04, 05) |
| 10 | MLE, entropy, Monte Carlo | MISSING (Monte Carlo in HW 07) |
| 11 | Transforms (MGF), CLT, sample stats | PARTIAL (HW 07) |
| 12 | Confidence intervals, hypothesis testing | MISSING |
| 13 | Optimal estimation, least squares | MISSING |
| 14 | Linear regression | MISSING |
| 15 | Logistic regression, neural classifiers | MISSING |
Recommendations
Homework Redistribution
HW 01-02: Keep as-is (well aligned)
HW 03: Move problems 10-14 to HW 04
HW 04:
- Keep Poisson/geometric problems
- Move problem 11 (Bayesian model selection) to new HW 09
- Move problem 16 (PGF) to new HW 11
HW 05:
- Keep continuous distribution problems (1-5, 7-13, 15-16)
- Move problem 0 (conjugacy) to HW 09
- Move problems 14, 17 (detection/hypothesis) to HW 12
- Move problem 19 (order stats) to HW 07
- Move problem 20 (mixtures) to HW 08
HW 06: Keep mostly as-is
HW 07:
- This HW covers Week 8 content, not Week 7
- Need NEW problems for Week 7: joint distributions, covariance, correlation
- Move current HW 07 content to HW 08
New Homework Needed
- HW 07 (new): Joint distributions, covariance, correlation, independence
- HW 08 (new): Multivariate normal, mixtures, LLN (can use some current HW 07)
- HW 09 (new): Bayesian statistics, conjugacy
- HW 10 (new): MLE, entropy, Monte Carlo
- HW 11 (new): MGF/transforms, CLT, sample statistics
- HW 12 (new): Confidence intervals, hypothesis testing
- HW 13 (new): Optimal estimation, least squares
- HW 14 (new): Linear regression