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3116Posterior Buy Probability After 7 Buys and 3 SellsA Bernoulli success probability p has prior Beta (2,3). After observing 7 successes and 3 failures, what is the posterior mean of p?统计简单derivation未尝试面试订阅3123Probability the Next Fill Is a SuccessA Bernoulli success probability has prior Beta (3,5). After observing 6 successes and 2 failures, compute the requested posterior predictive probability for the next 1 trial(s).统计中等derivation未尝试面试订阅3126Posterior Mean Arrival Rate After 12 Events in Two HoursA Poisson rate has prior Gamma (3,1) in shape-rate form. After observing 12 events over 2 hour(s), what is the posterior mean of ?统计中等derivation未尝试面试订阅3128Next-Hour Predictive Mean from Gamma-PoissonA Poisson rate has prior Gamma (4,1) in shape-rate form. After observing 5 events over 1 hour(s), what is the posterior predictive mean number of events in the next 1 hour(s)?统计中等derivation未尝试面试订阅3130Predictive Mean Trade Count in the Next Half HourA Poisson rate has prior Gamma (5,2) in shape-rate form. After observing 10 events over 4 hour(s), what is the posterior predictive mean number of events in the next 1 2 hour(s)?统计中等derivation未尝试面试订阅3131Posterior Mean of a Latent Fair ValueSuppose \sim N(0,4) and conditional on , you observe n=1 independent measurements with known variance 2=2 and sample mean x=3. Compute the posterior mean and posterior variance of .统计中等derivation未尝试面试订阅3133Posterior Mean from Three Noisy MeasurementsSuppose \sim N(-1,16) and conditional on , you observe n=3 independent measurements with known variance 2=1 and sample mean x=2. Compute the posterior mean and posterior variance of .统计中等derivation未尝试面试订阅3136Posterior Predictive Category ProbabilitiesA categorical distribution over three states has prior Dirichlet (2,3,5). After observing counts [4, 1, 5], what is the posterior predictive probability that the next observation is in category 1?统计中等derivation未尝试面试订阅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6017Posterior Distribution After Ten Wins in TwelveA win probability p has the uniform prior Beta (1,1). You then see k=10 wins out of n=12 games. Name the exact posterior distribution of p and give its mode.统计简单数值题未尝试免费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6019Blending a Prior View With Four Noisy QuotesA latent fair value \sim N(10,4). You collect n=4 independent quotes with known per-quote variance 2=8 and sample mean x=12. Compute 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6022MAP Estimate Versus Posterior MeanAfter updating, the posterior for a conversion rate p is Beta (8,4). Report both the MAP (posterior mode) estimate and the posterior mean, and state which is larger.统计中等derivation未尝试免费