algorithm importance sampling estimation inputfunction himportance sampling density such that ( for all for which (xf ( sample size nconfidence level outputpoint estimate and approximate ( aconfidence interval for eh( )where iid simulate and let yi ( ( )/ ( ) estimate via and determine an approximate ( aconfidence interval as - / : - / where zg denotes the -quantile of the ( distribution and is the sample standard deviation of yn return and the interval example (importance samplinglet us examine the workings of importance sampling by estimating the areau sayunder the graph of the function + sin ( ( ( we saw similar function in example (but note the different domaina natural approach to estimate the area is to truncate the domain to the square [-bb] for large enough band to estimate the integral bz ub ( ) (xf (xdx ( { - - (xvia crude monte carlowhere ( /( ) [-bb] is the pdf of the uniform distribution on [-bb] here is the python code which does just that impsamp py import numpy as np from numpy import exp sqrt sin pi log cos from numpy random import rand lambda ( * )** exp(-sqrt( ** ** / *sin ( sqrtx ** ** ))+ * ** ** ** /(( )** ** - * *rand( , - * *rand( , ( , estcmc np mean(zitem (to obtain scalar recmc np std( )estcmc /sqrt(nitem (print ('ci ({: ,{: }re { }format estcmc *( - recmc )estcmc *( + recmc ),recmc )ci ( , re