Exercise 1 (25 points): 1. Consider a set of d-dimensional points X-[^i,... .zn] and distance function Show that the representative IiEX is the mean of the points in X. That is, for every 1 e {1, , d)-"(1)---,-i(1). (10 points) 2. Consider a set of d-dimensional points X-[x1,... . xn] and distance function Show that the representative r-arg min Di(zi, z) T arg IiEX is the median of the points in X. That is, for every (15 points) f1,.,demedian(ri(e).r()) Exercise 1 (25 points): 1. Consider a set of d-dimensional points X-[^i,... .zn] and distance function Show that the representative IiEX is the mean of the points in X. That is, for every 1 e {1, , d)-"(1)---,-i(1). (10 points) 2. Consider a set of d-dimensional points X-[x1,... . xn] and distance function Show that the representative r-arg min Di(zi, z) T arg IiEX is the median of the points in X. That is, for every (15 points) f1,.,demedian(ri(e).r())