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Assessment Solutions and Scoring

Use only after an attempt. Award the model point only when the sampling/stopping assumptions are explicit, and the interpretation point only when the requested distinction is explained. A correct unsupported number earns at most the two calculation points.

  1. PS1: selected-position protocol gives (1/4)/(1/2)=1/2; at-least-one protocol gives1/3. Model point: distinguish the observation likelihoods. Derivation points: correct reweighting and both results. Interpretation: reporting protocol changes the event conditioned on.
  2. PS2: defect400:300 flagged,100 missed; nondefect9,600:192 flagged,9,408 unflagged. Precision=300/492=25/41≈.609756, sensitivity=.75. Model: correct populations. Derivation: table and precision. Interpretation: different denominators.
  3. PS3: expected attempts1.11,failures.111,backoffs.11,success.999. Model: three total attempts, independent constant p, stop on success. Derivation: indicator sums and numbers. Interpretation: maximum attempts differs from three always-executed trials.
  4. PS4: ten unordered samples; PMF for k=0,1,2 is3/10,6/10,1/10. Mean=.8; E[X²]=1; variance=.36. With replacement: Binomial(2,.4), mean=.8,variance=.48. Model: equal-probability samples. Derivation: PMF and moments. Interpretation: dependence changes variance.
  5. PS5: variance=(4+4+2*3)/4=3.5; independent case=2. Model: retain covariance. Derivation: sum variance and scaling. Interpretation: positive covariance reduces the benefit of averaging.
  6. PS6: density1/4 on[0,4],interval probability1/2,mean2,variance16/12=4/3,lower99th quantile3.96. Model: normalized density. Derivation: interval and moments/quantile (one point each). Interpretation: zero-width points have zero probability despite a nonzero density.
  7. PS7: LLN gives convergence of averages under integrability; independent variance algebra gives sigma²/n; the CLT gives asymptotic Normality of the standardized mean. Twenty independent nonfailures have positive probability (1-p)^20 for every p below1, so they do not identify p=0. Coverage is the probability a random interval contains the fixed parameter under repeated sampling; nominal95% may differ from actual finite-sample coverage. Model: correct assumptions. Derivation: distinguish exact variance from limiting shape and explain the zero-count evidence. Interpretation: correct coverage language.
  8. PS8: raw A91,B21.8 ms; standardized A55,B61 ms. One defensible plan randomizes sessions to versions, records all requests including timeouts, and stops at a predeclared number of independent sessions. State a target workload and analyze within-session dependence. Missing information includes assignment, within-group variability, environment, timestamps, and selection. Model: shared target and sampling unit. Derivation: both pairs of means. Interpretation: no causal conclusion from this aggregate fixture alone.

Transfer feedback for self-study​

For an at-most-four-attempt model at p=.2, the values in practice B2 apply. If failures instead share one common outage event of probability .2 and otherwise always succeed, four attempts succeed with probability .8, not .9984; expected attempts are .8*1+.2*4=1.6. For two samples with replacement from five nodes with two faults, the PMF is .36,.48,.16. Replacing request randomization with session randomization changes the experimental unit and variance analysis, not merely a column name.

A reviewer should change numbers and the dependency model again once these solutions have been seen. Code output or memorized values do not replace a fresh derivation.