2nd Edition 3.54

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2nd Edition 3.54

Postby Paul2906 » Fri Sep 26, 2014 4:12 pm


I think that there is a typo in the answer of the question 3.54.

If Z_1 ~ N(0,1), then W_1 = a Z_1 ~ N(0,a^2).

Besides, considering that (X,Y) is a gaussian vector with mean 0, we should have:

E[X|2X+Y] = E[X(2X+Y)]/E[(2X+Y)^2] x (2X+Y)

with E[X(2X+Y)] = 2a + rho sqrt(ab)
E[(2X+Y)^2] =4a + b + 4 rho sqrt(ab)

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Re: 2nd Edition 3.54

Postby tns » Sat Jun 24, 2017 8:41 pm

Indeed, seems like standard deviation and variance are mixed up in the solution.

Also the solution assumes that X and Y can be written as a linear combination of the same independent normal random variables, i.e. that X and Y are jointly normal. This is smth that is not clearly stated in the Question.
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