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1. The mean and variance of a population 9 = {3:1, ...yN} measure the centre and the spreadfvariability of the population, respectively. Excess kurtosis is another attribute which measures how heavily the tails of the distribution differ from the tails of a standard normal distribution. From the several different methods to measure the kurtosis, we use the following two methods in this question: 31102: rm T '3' where I7 is the mean, and S 4 is the square of the variance. 01(93): Qs-Qi =--.2 17 052'?) 2(P1oP9o) 0 6 ' where QI- is the i\"! quartile and Pi is the i\"1 percentile. Consider the simulated population pop dened below: set.seed(Your UH ID Number) pop = rt(100,2) (a) [3 marks] Draw the probability histogram (area = 1) of the data and superimpose on this his- togram the probability density curve of the standard normal distribution. Based on this plot, what do you conclude about the kurtosis of the simulated population? Note: see the help document of the hist function for proper scaling of the area of the histogram. (b) [4 marks] Plot 8010;) and 80200, the sensitivity curves of alt?) and 052(9'), respectively, for y E [15,15] based on the simulated population above. (c) [2 marks] Based on the plot in part (b), which kurtosis attribute is more desirable, and why? Provide one reason why one may use the attribute which is inferior based on the plot in part (b). (d) [3 marks] Which of the two attributes ail-(J, i = 1,2 has a higher breakdown point? Justify your