Consider the following procedure:

A fair die is tossed to generate X {1,2,...,6}. X fair coins are then tossed. Y is the number of heads.

Suppose you observe only X. Find the MMSE estimate of Y given X.

Need detailed steps for all three questions

1. Suppose x1,,xnN(,2) i.i.d. with known variance 2. Find the MLE of . 2. Consider the following procedure: - A fair die is tossed to generate X{1,2,,6}. - X fair coins are then tossed. Y is the number of heads. Suppose you observe only X. Find the MMSE of Y given X. 3. Explain each line of the following code snippet. \( \begin{array}{ll}1 & \text { model = LinearRegression() } \\ 2 & \text { poly_features = PolynomialFeatures(degree=d, include_bias=True) } \\ 3 & \text { Xtrain_poly = poly_features.fit_transform(Xtrain) } \\ 4 & \text { model.fit(Xtrain_poly, ytrain) }\end{array} \)