number in the sample who were in favor of the prop- osition.

Extracted text: number in the sample who were in favor of the prop- osition.


Extracted text: 12. Let 0 denote the proportion of registered voters in a large city who are in favor of a certain proposition. Sup- pose that the value of 0 is unknown, and two statisticians A and B assign to 0 the following different prior p.d.f's ŠA(O) and Šp(0), respectively: ŠA(O) = 20 for 0 < 0="">< 1,="" šb(0)="403" for="" 0="">< 0="">< 1.="" in="" a="" random="" sample="" of="" 1000="" registered="" voters="" from="" the="" city,="" it="" is="" found="" that="" 710="" are="" in="" favor="" of="" the="" proposition.="" a.="" find="" the="" posterior="" distribution="" that="" each="" statistician="" assigns="" to="" 0.="" b.="" find="" the="" bayes="" estimate="" for="" each="" statistician="" based="" on="" the="" squared="" error="" loss="" function.="" c.="" show="" that="" after="" the="" opinions="" of="" the="" 1000="" registered="" voters="" in="" the="" random="" sample="" had="" been="" obtained,="" the="" bayes="" estimates="" for="" the="" two="" statisticians="" could="" not="" possibly="" differ="" by="" more="" than="" 0.002,="" regardless="" of="">