150 Petridishespreparedwithstreptomycinwereeachsubjectedto one millionE-colibacteria.Ifabacteriummutatestobecomeresistant,itwillgrowa colonyofsurvivingbacteria.Otherwisethestreptomycinwillkillthebacteria.After growth,thefollowingnumberofsurvivingcolonieswasobserved:

a) ArguewhyitwouldbereasonabletoexpectthatthenumberofcoloniesinaPetri dish wouldbePoissondistributed;

b) EstimatetheparameterundertheassumptionofaPoissondistributednumberof colonies.

c) InvestigatewhethertheobservationsconformwiththePoissonmodel.

Note thatasthePoissondistributionhasinfinitesupport,alittlemodificationis needed totransformthedataintoamultinomialdistributiontoanswerquestionc).
This may,forexamplebedonebymergingthecategories 3, 4, ... into acategory ≥ 3 with acountof4,orevenmergingto ≥ 2 with acountof12.Thisnowbecomes a curvedmultinomialfamily,andtheanalysismayproceedalongthesamelinesas in Example8.2.

Transcribed Image Text:

Number of colonies per dish 0 1 2 3 4 Number of Petri dishes 98 40 8 3 1