Assignment using R

(5 points)

For each of p =50, 100, 500, 1000, randomly draw n = 10000 pairs of independent points uniform in the cube in p-space, [0,1]p. Then for each pair of two points calculate the distance. Use the n distances to calculate the ratio

r = 25th percentile of the distances / 75th percentile of the distances . Simulate the process for s = 1000 times to obtain r1,r2,,rs and make 95% confidence limit of the ratio's for each p. Draw a plot to show the pattern of the 95% confidence limits when p increases and explain. Note that 95% confidence limit is the interval of (2.5th percentile, 97.5th percentile).

Thank you