- #1
bennyska
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Homework Statement
in a genetics situation, we have two variables, x1 and x2, such that both x1 and x2 >0, and x1+x2<1.
we have:
p1 = x12
p2 = x22
p3 = (1-x1-x2)2
p4 = 2x1x2
p5 = 2x1(1-x1-x2)
p6 = 2x2(1-x1-x2)
find the mles for x1 and x2.
Homework Equations
the answer (from the book): x1(hat) = (2N1 + N4 + N5)/2n, where n = sum (Ni). x2(hat) is similar.
The Attempt at a Solution
doing the usual mle stuff, i have sum(Ni*ln(pi)), take the derivative, set to zero, and solve for my parameter. when i do this work, i get an answer similar (but incorrect) to that of the book, with a little problem: in order to get n, i need all the Nis. when i take the derivative with respect to x1, there is one term (p2) that doesn't have x1 in it, so it drops out, and i lose that term (N2) that i think i need. i can't define x1 by x2 (i think, since x1 + x2 < 1 doesn't tell me too much). my teacher assigned this one to us, without having done the problem herself, and then she found herself unable to do it. we figure there's some little trick involved, but I'm not seeing it. also, i haven't really done mles with more than one variable, so maybe that's what I'm missing. any help would be greatly appreciated.