We consider the following three sample functions m = 12 (k+1) (8)+(+1) for n = 2k + 1 odd for n = 2k even -1 1 = < 1) ( - m 11 (7 - m < 1) where (1) (2) (n) denote the ordered values of n observations We are interested in the sampling distribution of m, and + under the as- sumption that x1,...,xn are realizations of real stochastic variables X1,..., Xn on (F,P) which are i.i.d. with distribution P. Here, can be regarded as a natural estimator for the median of P, while is a natural estimator for the mean of P. can be regarded as an estimator for the mean of P, which only uses the observations near the median. 1. Calculate m, and + based on 21,...,n. Then use non-parametric boot- strap to approximate the sampling distribution for these three sample functions. Please visualize the bootstrap distributions and determine 95% confidence intervals. 2. Provide examples of what can be said about probabilities of the form: P(> 0.2) for at least one of the following distributions: P is the uniform distribution on [-1, 1]. P is a normal distribution with mean 0 and variance 1. P is a Laplace distribution with density f(x) = e|| It would be obvious to start with a version of Chebyshev's inequality