Exercise2.18 A largetelephonecompanywantstoestimatetheaveragenumberofdailytelephone calls madebyitsprivateclients.Itisknownthatontheaveragewomenmake a times morecalls than men.ItisreasonabletoassumethatthenumberofdailycallshasaPoissondistribution.During a certainday,thecompanyregisteredthenumbersofdailycallsmadeby n female and m male randomly-chosen clients.

1. What isthestatisticalmodelforthedata?Doesthedistributionofthedatabelongtotheexpo-

nential family?

2. Find theMLEfortheaveragedailynumberofcallsmadebyfemaleandmaleclients.

3. Are theMLEsfromthepreviousparagraphunbiased?