Consider a random sample X1, X2, . . . , Xn from a distribution with pdf
Let θ have a prior pdf that is gamma with α = 4 and the usual θ = 1/4. Find the conditional mean of θ, given that X1 = x1, X2 = x2, . . . , Xn = xn.
Answer to relevant QuestionsLet Y be the largest order statistic of a random sample of size n from a distribution with pdf f(x | θ) = 1/θ, 0 < x < θ. Say θ has the prior pdf where α > 0, β > 0. (a) If w(Y) is the Bayes estimator of θ and [θ − ...A leakage test was conducted to determine the effectiveness of a seal designed to keep the inside of a plug airtight. An air needle was inserted into the plug, and the plug and needle were placed under water. The pressure ...Assume that the yield per acre for a particular variety of soybeans is N(μ, σ2). For a random sample of n = 5 plots, the yields in bushels per acre were 37.4, 48.8, 46.9, 55.0, and 44.0. (a) Give a point estimate for ...A candy manufacturer selects mints at random from the production line and weighs them. For one week, the day shift weighed n1 = 194 mints and the night shift weighed n2 = 162 mints. The numbers of these mints that weighed at ...Let Y1 < Y2 < · · · < Y8 be the order statistics of eight independent observations from a continuous-type distribution with 70th percentile π0.7 = 27.3. (a) Determine P(y7 < 27.3). (b) Find P(Y5 < 27.3 < Y8).
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