{"title":"Quiz","authors":"J. Hunt","doi":"10.4324/9781003122296-7","DOIUrl":null,"url":null,"abstract":"A fancy new restaurant has opened up that features only 4 dishes. The unique feature of dining here is that they will serve you any of the four dishes randomly according to the following probability distribution: give dish A with probability 0.5, dish B with probability θ, dish C with probability 2θ, and dish D with probability 0.5 ́ 3θ. Each diner is served a dish independently. Let xA be the number of people who received dish A, xB the number of people who received dish B, etc, where xA ` xB ` xC ` xD “ n. Find the MLE for θ, θ̂.","PeriodicalId":306258,"journal":{"name":"Sex Ed for Grown-Ups","volume":"62 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sex Ed for Grown-Ups","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4324/9781003122296-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
A fancy new restaurant has opened up that features only 4 dishes. The unique feature of dining here is that they will serve you any of the four dishes randomly according to the following probability distribution: give dish A with probability 0.5, dish B with probability θ, dish C with probability 2θ, and dish D with probability 0.5 ́ 3θ. Each diner is served a dish independently. Let xA be the number of people who received dish A, xB the number of people who received dish B, etc, where xA ` xB ` xC ` xD “ n. Find the MLE for θ, θ̂.
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