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6013Power of a One-Sided Z-TestYou run a one-sided z-test at level alpha = 0.05 (critical value 1.645) for a positive mean edge. The true edge is delta = 3 bp, the per-observation standard deviation is sigma = 8 bp, and you collect n = 64 observations. The power equals Phi(delta*sqrt(n)/sigma - 1.645). Compute the power, using Phi(1.355) approx 0.9123.统计中等数值题未尝试免费6016Posterior Mean Hit Rate After a Cold StreakA signal's hit probability p has prior Beta (4,4). Over the next batch you record 3 hits and 9 misses. By integrating the posterior density, what is the posterior mean of p?统计简单derivation未尝试免费6018Posterior Mean Rate for a Rare FaultFaults arrive as a Poisson process with rate per day, prior Gamma (2,0.5) in shape-rate form. Over 3.5 days you observe 7 faults. What is the posterior mean of ?统计中等derivation未尝试免费6020Predictive Chance the Next Trade FailsA fill probability p has prior Beta (2,1). After observing 3 fills and 4 misses, what is the posterior predictive probability that the very next attempt is a miss (a failure)?统计中等derivation未尝试免费