Inference reviewer calibration

Use only after an independent attempt; alternate valid derivations earn credit.

• PS9: transformed CDF y^(1/4) on [0,1], density (1/4)y^(−3/4) inside, mean 1/5. For the triangular joint, marginal 2(1−x), conditional mean (x+1)/2 for 0<x<1. Product support is wrong for independence. CDF endpoints and zero density outside support must be explicit.
• PS10: n=4, sum=16, rate 1/4 per duration unit. Log likelihood 4 ln λ−16λ is strictly concave for λ>0. All-zero data have no finite maximizer; right-censored observations require survival contributions rather than deletion.
• PS11: Beta(5,7), next-trial success probability 5/12. Separate model: Beta(1,4), density 4(1−p)³, CDF 1−(1−p)^4, upper limit 1−0.05^(1/4), about 0.527. State the prior and sampling assumptions; this posterior statement is not an automatic long-run coverage claim.
• PS12: observed sum 7 and mean 7/4. Four of sixteen assignments attain absolute sum at least 7, because the zero contributes two assignments for each common sign of the positive entries. Thus p=1/4. The assignment design, sharp null, prespecified tail rule and tie multiplicities are necessary. Inspect actual code and reports, then change the dataset without revealing this key.

Review checks do not establish learner calibration. Request independent statistics review before describing these gates as externally validated.