fr ( for respectively(bexplain how to simulate using the inverse-transform method (csimulate independent draws of [xy]according to the method described above simple acceptance-rejection method to simulate vector in the unit -ball { rd kxk is to first generate uniformly in the hyper cube [- ] and then to accept the point only if kxk determine an analytic expression for the probability of acceptance as function of and plot this for let the random variable have pdf xf ( simulate random variable from ( )using (athe inverse-transform method(bthe acceptance-rejection methodusing the proposal density ( construct simulation algorithms for the following distributionsa (athe weib(aldistributionwith cdf ( -(lxx where and (bthe pareto(aldistributionwith pdf (xal( lx)-( + where and we wish to sample from the pdf (xx - using acceptance-rejection with the proposal pdf (xe- / / (afind the smallest for which cg(xf (xfor all (bwhat is the efficiency of this acceptance-rejection method let [xy]be uniformly distributed on the triangle with corners ( )( )and (- give the distribution of [uv]defined by the linear transformation # explain how to generate random variable from the extreme value distributionwhich has cdf - ( eexps via the inverse-transform method ( )