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In: Statistics and Probability

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the...

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the following estimator of the intercept of the Best Linear Predictor:

A = ?̅ - B • ?̅ ,
where ?̅ is the sample mean of y, ?̅ is the sample mean of x, and B is the sample covariance of Y and X divided by the sample variance of X.

Identify the probability limit of A (if any). For each step in your derivation, you must refer to the specific theorems on which that step in your derivation relies.

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Expert Solution

It is hereby assumed that E(X), E(Y), Var(X), Var(Y) exists finitely and Var(X) and Var(Y) are strictly positive.

orchestra answered 2 years ago
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