29 we will often be interested in e y 2 x x as we saw

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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. 30
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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. 31
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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 . 32
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