Re: Expected return & variance of a bivariate distribution

Jack Tomsky wrote:

I'm stuck with a problem that is easy to solve if I
assume that the
bivariate distribution is normal or some other type
of distribution.
However, since it's not stated what the
distribution,
I'm not sure
I've enough information to work with. I'm given
that
it's a bivariate
distribution with the 2 means and standard
deviations
given, as well
as the correlation. I'm then asked to work out the
expected value and
standard deviation of the first given the expected
value & standard
deviation of the second.

Without being given the type of distribution or
making an assumption,
I could calculate the covariance and E(XY) at best.
Am I right or did
I miss something else?



I'm assuming that the question should be phrased in
terms of the conditional mean and condition variance
of X, given Y.

E(X|Y) = mux + (cov(X,Y)/Var(Y))*(Y-muY)
Var(X|Y) = Var(X) - (Cov(X,Y)^2)/Var(Y)



Those formulae hold only when X and Y are jointly
normal. In
general, the OP is correct. Without further
information about the joint
distribution, the means and covariance matrix do not
provide sufficient
information to compute the conditional mean and
variance.


--
Stephen J. Herschkorn
sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey
and Manhattan


Steve, you're right. I read the question a little too fast. I read "if I assume that the bivariate distribution is normal" and assumed that this was a given.

Jack
.

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