Question

Consider a classification setting with 2 classes and 1 predictor. When we use the Bayes classifier, we assign an observation to the class receiving the highest conditional probability Pr(Y=k|X=x). The Bayes decision boundary is such that Pr(Y=1|X=x) = Pr(Y=2|X=x). It gives the values of the variable X for which we have an equal probability. With LDA, you can find the Bayes decision boundary using the LDA δ(x). Find this decision boundary by assuming equal priors and constant variance σ^2 across classes. You will need to compute δ1(x) and δ2(x). Show all your work. What does this boundary look like when the mean of X in class one is -1.25 while the mean of X in class two is 1.25?

          Consider a classification setting with 2 classes and 1 predictor. When we use the Bayes classifier, we assign an observation to the class receiving the highest conditional probability Pr(Y=k|X=x). The Bayes decision boundary is such that Pr(Y=1|X=x) = Pr(Y=2|X=x). It gives the values of the variable X for which we have an equal probability. With LDA, you can find the Bayes decision boundary using the LDA δ(x). Find this decision boundary by assuming equal priors and constant variance σ^2 across classes. You will need to compute δ1(x) and δ2(x). Show all your work. What does this boundary look like when the mean of X in class one is -1.25 while the mean of X in class two is 1.25?

Added by Maria R.

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