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∙
We will often be interested in
E
Y
2

X
x
.
∙
As we saw in the example of an exponential distribution, if we
construct conditional distributions from the unconditional distributions
we already know, then finding conditional moments is trivial.
∙
In many applications, the main feature that we must specify
is
the
conditional mean. Often fairly simple forms are used, such as
E
Y

X
x
x
E
Y

X
x
x
x
2
and so on.
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∙
If
X
is a random vector, linearity is often assumed:
E
Y

X
x
1
x
1
...
k
x
k
≡
x
where
x
x
1
,
x
2
,...,
x
k
is a row vector.
∙
Often
X
contains nonlinear functions of underlying variables. In EC
820B, you will see that it is linearity in the parameters
and
that has
consequences for estimation.
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Generally, if we write
E
Y

X
x
x
then we are interested in
knowing how
x
changes as the elements of
x
change. Often, at least
for continuous elements, we focuse on the partial derivatives,
∂
x
∂
x
j
.
For discrete changes, we can look at differences evaluated at two values
of
x
.
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