TheHardyWeinbergformulaforthegeneticvariationofapopulationatequilibriumstatesthat with probability of the A allele, theprobabilitiesofgenotypes(AA, Aa, aa) are (2, 2(1 ), (1)2).
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TheHardy–Weinbergformulaforthegeneticvariationofapopulationatequilibriumstatesthat with probability π of the A allele, theprobabilitiesofgenotypes(AA, Aa, aa) are (π2, 2π(1 −
π), (1−π)2). Assumeamultinomialdistribution(Section 2.6.4) for n observationswithcounts
(y1, y2, y3) of (AA,Aa,aa).
(a) Expressthelog-likelihoodfunctionforthemultinomialandfindtheMLestimateof π.
(b) Usingequation(4.4),find I(π) and theapproximatelarge-samplestandarderrorof ˆπ.
(c) Explainhowyoucouldusethelarge-samplenormalityofMLestimatorsandtheresult in (b)toconstructa95%confidenceintervalfor π.
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Related Book For 
Foundations Of Statistics For Data Scientists With R And Python
ISBN: 9780367748456
1st Edition
Authors: Alan Agresti
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