Important measures in exploratory data analysis are the skewness 71 = E(X-E(X))3 and the kurtosis 72 = E(X-E(X) )4 Var (X) 3/2 Var ( X ) 2 - 3. One way of estimating them is by using their empirical counterparts 71 = Vn En (Xi-X) 3 (E (Xi-X)2)3/2 and 72 = -n E (X1-X)4 (E (X1-X)2)2 - 3, respectively. a) Write down two R functions myskewness and mykurtosis to get 71 and 72- b) Load Library MASS in R and find the data cats. The third column in this data frame describes the body weights of 144 cats taken during a digitalis experiment. Use your functions to estimate 71 and 2 for the body weights. c) Bootstrap the 71 and 72 estimators by using B = 5000 replicates and report the resulting 95% confidence intervals using first principles. d) For a normal population, theoretical skewness and kurtosis are both equal to zero. If the 95% confidence interval for either skewness or kurtosis excludes zero, the normality is in doubt. What is your conclusion about the normality of the body weights of these cats? Double check your claim graphically using qqnorm. Include your coding, and the output containing the confidence intervals, in your assignment