## Question

###### 1. Suppose you have one continuous predictor X and binary categorical rcsponse Y which can takc valucs or 2. Suppose you collected train- ing data from the two classes and obtained class-specific sample means and p2 along ` with the pooled variance estimatc over the two classcs_ 1. (AOpt total, Spt for cach question)Assume equal class priors and derive the LDA classification rule for this problem_ Sketch the estimatcd class-conditional densitics and show your decision boundary on the plot Make

1. Suppose you have one continuous predictor X and binary categorical rcsponse Y which can takc valucs or 2. Suppose you collected train- ing data from the two classes and obtained class-specific sample means and p2 along ` with the pooled variance estimatc over the two classcs_ 1. (AOpt total, Spt for cach question) Assume equal class priors and derive the LDA classification rule for this problem_ Sketch the estimatcd class-conditional densitics and show your decision boundary on the plot Make sure you labcl the axes and indicate the numcrical valuc for the boundary; let'$ call it Suppose the estimates were in fact obtained from 100 training points among which 40 were from class and 60 wcrc from class Suppose now you will estimate class priors from data, repeat all the calculations in part and obtain new boundary valuc, let s call it : Without actually doing this would you be able to tell whether will be thc same as less than Or greater than is there no way to tell? Explain your answer without calculating Note: It s ok to recheck your answer once YOu have actually calculate in part (c); but your explanation must not involve the numcrical valuc Now calculate the new boundary value â‚¬ described in Part (6). Suppose in addition to the pooled covariance value &2 now tell you the individual class specific covariances wCrC estimated = 0.25 and 63 =15. Based on this nw information_ would yoU recommend using LDA or QDA and why? Derive the QDA rule for purt (d) , assuming equal class priors.