Consider a population made up of three different types of individuals occurring in the Hardy-Weinberg proportions B2 , 2B(1 - B) and (1 - B)2, respectively, where 0< B < 1. (a) Show that T3 = N1/n + N2/2n is a frequency substitution estimate of B. (b) Using the estimate of (a), what is a frequency substitution estimate of the odds ratio B/(l - B)? (c) Suppose X takes the values -1,0,1 with respective probabilities PI,P2,P3 given by the Hardy-Weinberg proportions. By considering the first moment of X, show that T3 is a method of moment estimate of B
Consider a population made up of three different types of individuals occurring in the Hardy-Weinberg proportions B2 , 2B(1 - B) and (1 - B)2, respectively, where 0< B < 1. (a) Show that T3 = N1/n + N2/2n is a frequency substitution estimate of B. (b) Using the estimate of (a), what is a frequency substitution estimate of the odds ratio B/(l - B)? (c) Suppose X takes the values -1,0,1 with respective probabilities PI,P2,P3 given by the Hardy-Weinberg proportions. By considering the first moment of X, show that T3 is a method of moment estimate of B
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Consider a population made up of three different types of individuals occurring in the
Hardy-Weinberg proportions B2 , 2B(1 - B) and (1 - B)2, respectively, where 0< B < 1.
(a) Show that T3 = N1/n + N2/2n is a frequency substitution estimate of B.
(b) Using the estimate of (a), what is a frequency substitution estimate of the odds ratio
B/(l - B)?
(c) Suppose X takes the values -1,0,1 with respective probabilities PI,P2,P3 given
by the Hardy-Weinberg proportions. By considering the first moment of X, show that T3
is a method of moment estimate of B
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