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1626Recovering a Three-Point Support Scale From Two MomentsA random variable takes values 0, a, and 3a with probabilities 1-2p, p, and p. If the empirical first two raw moments are m 1 and m 2, solve for a and p by method of moments.统计简单derivation未尝试免费1627Sparse Symmetric Shock Model From Variance and Fourth MomentA symmetric shock variable takes values -a, 0, and a with probabilities p, 1-2p, and p. If the sample second and fourth raw moments are m 2 and m 4, solve for a and p by method of moments.统计中等derivation未尝试免费1628Estimating a Zero-Inflated Order-Arrival ModelPer-second order arrivals are modeled as follows: with probability the market is inactive and the observed count is exactly 0; with probability 1- , the count is Poisson ( ). From data, the empirical zero frequency is 0.70 and the empirical mean count is 0.60. Use the method of moments to estimate ( , ).统计困难derivation未尝试面试订阅1629MoM for a Random Amplitude Bernoulli CountLet X=AZ where Z is Bernoulli with success probability p and the success amplitude A is a positive constant. If the sample mean is m 1 and the sample second raw moment is m 2, solve for A and p.统计中等derivation未尝试免费1630Shifted Exponential Calibration from Raw MomentsA toy latency model assumes X = c + Y, \qquad Y \sim Exp ( ), with unknown deterministic floor c>0 and unknown rate . From historical data, the empirical mean of X is 8 and the empirical second raw moment is 73. Use the method of moments to estimate c and .统计简单derivation未尝试免费1631Recovering Latent Regime Size from Second and Fourth MomentsA stylized one-period microstructure model writes the observed shock as Y = S a + \varepsilon, where S takes values +1 and -1 with equal probability, a>0 is an unknown regime magnitude, and \varepsilon \sim N(0, 2) is independent noise. From data, the empirical second moment is m 2 = 5 and the empirical fourth moment is m 4 = 43. Use the method of moments to estimate a and 2.统计困难derivation未尝试面试订阅1632Estimating Activity and Size in a Zero-Inflated Fill ModelConsider a toy fill-size model for a child order. With probability 1-p, no fill occurs and the observed size is 0. With probability p, a fill occurs and the size is exponentially distributed with rate . The empirical mean fill size is 2 and the empirical variance is 12. Use the method of moments to estimate p and .统计困难derivation未尝试面试订阅1633Two-Rate Latency Mixture With Known Mixing WeightA latency variable is a 50-50 mixture of two exponential laws with rates \lambda 1 and \lambda 2. The first two raw moments are m 1 and m 2. Write the two equations that method of moments imposes on (\lambda 1,\lambda 2).统计中等derivation未尝试面试订阅1634Inferring Cross-Day Heterogeneity from Paired Signal OutcomesSuppose each trading day has an unobserved hit probability P \sim Beta ( , ). Conditional on P, two independent intraday signals H 1 and H 2 are Bernoulli(P). From data, you estimate E[H 1] = 0.60, \qquad P(H 1=1, H 2=1) = 0.42. Use the method of moments to estimate and .统计中等derivation未尝试面试订阅1635Estimating a Three-Point Shock Model from Even MomentsA stylized inventory-shock model assumes the one-step PnL jump X takes values -a, 0, and +a with probabilities p/2, 1-p, and p/2, respectively, where a>0 is unknown. From data, the empirical second moment is 2 and the empirical fourth moment is 10. Use the method of moments to estimate p and a.统计简单derivation未尝试免费