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4.2 Mixture of normals Suppose that n pairs (2;, vi), i = 1, ...,n, are independently drawn from the following mixture of normals distribution: with probability p. with probability 1 - p, where 0 0. The parameters or, S and y are not known. A random sample of observations on (y, 2, w) is available; z is not observable. In this setting, a researcher weighs two options for estimating 8. One is a linear least squares fit of y on r. The other is a linear least squares fit of y on (a, we). Compare these options. 2. Let (z, W. 2) be a random triple. For a given real constant y, a researcher wants to estimate E[vE (x=] = v. The researcher knows that E (x(=] and E [y|=] are strictly increasing and continuous functions of z, and is given consistent estimates of these functions. Show how the researcher can use them to obtain a consistent estimate of the quantity of interest