Solved Problems - Probability and Statistics for Electrical Engineering | STAT 4714, Assignments of Probability and Statistics

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STAT 4714 Answers to the Problems on Bayesian Estimation 1. Use the approach in Example 1. Ag] RADE (DA C6 P rs) (a) In a random sample of m= 20 customers, only 11 preferred the new display, so the MLE of pis Pyge =11/20=.58. (b) First calculate the posterior probability for 0.5, given that ¥ =11. (20) | Josten” (2) ats eee (20) uy oo (20) atv) 20) uy 99 sys)? Cay] Lent cay? coy] © [ecu cay uit (tl Mtl) 52006 = 449511 * (032036 -+.039228 +.000011 Proceeding in this way tu calculate a(.7|11) and #(.9|11) gives P 5 7] 8 ‘py 44gsi1 | 553i | coos {c) The Bayes estimator of p is E(o| X=11)= (5449511) + (7550341) = 91.000 148) =.6101 This value is above the MLE value of 55, 2. Use the approach in Example 2. {8 pis) (a) Find the density of the posterior distribution. l@ pi'(t— py? -252p°a- py alp|X=1)= a =p}? :252p"(1— py dp 29s - eee d-p)!, Oxpei (b) The Bayes estimator of p is