3. Suppose you have one continuous predictor X and a binary categorical re- sponse Y, which can take values 1 or 2. Suppose you collected training data from the two classes and obtained class-specic sample means [11 = 1 and ag = 3, along with the pooled variance estimate over the two classes, 62 = 1. (a) (6) Assume equal class priors and derive the LDA classication rule for this problem. Sketch the estimated class-conditional densities and show your decision boundary on the plot. Make sure you label the axes and indicate the numerical value for the boundary; let's call it (2. Suppose the estimates were in fact obtained from 100 training points, among which 40 were from class 1 and 60 were from class 2. Suppose now you will estimate class priors from data, repeat all the calculations in part (a) and obtain a new boundary value, let's call it E. Without actually doing this, would you be able to tell whether 5 will be the same as, less than, or greater than c, or is there no way to tell? Explain your answer without calculating 5. Note: It's ok to recheck your answer once you have actually calculate 5 in part (c), but your explanation must not involve the numerical value. Now calculate the new boundary value 5 described in part (b). Suppose in addition to the pooled covariance value 62 I now tell you the individual class specic covariances were estimated as 6% = 0.25 and 62 = 1.5. Based on this new information, would you recommend using LDA or QDA, and why? Derive the QDA rule for part ((1), assuming equal class priors