Show that the following are equivalent metrics for Rn: (i) d1 (x, y) = || x – y ||1 = {n∑i=1 (xi – yi)2}(1/2);

(ii) d2 (x, y) = || x – y ||2 = max1 ≤ i ≤ n |xi – yi|;

(iii) d3 (x, y) = || x – y ||3 = n∑i=1 |xi – yi|.

Needmax recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.