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#This imports all the packages \ou need for the homeZork
#Please run this first
import QXmS\ as QS

import VciS\.VSecial as VSVS

import maWSlRWlib.S\SlRW as SlW

%maWSlRWlib iQliQe

import V\mS\

import VciS\.VWaWV as VSVW
import VimS\
import cRS\
!SiS iQVWall h\SeURSW -T
import h\SeURSW
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#generate Bt, an arra\ that giYes Bt Yalue for each t Yalue in t_arra\
def B_W(W):
return BW

##run the B_t(t) 5 times and plot the trajector\ for each case
QS.UaQdRm.Veed(10)

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#generate S_t
def S_W(W,a, mX, Vigma2):
return SW


##run the S_t(t) 5 times and plot the trajector\ for each case
QS.UaQdRm.Veed(10)

#Zithout using Yariance reduction
QS.UaQdRm.Veed(10)



#antithetic method
QS.UaQdRm.Veed(10)

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##Zithout Yariance reduction
QS.UaQdRm.Veed(10)

#Common random number
QS.UaQdRm.Veed(10)


QS.UaQdRm.Veed(10)

#control Yariate
QS.UaQdRm.Veed(10)

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#importance sampling
QS.UaQdRm.Veed(10)

##h\opt to find optimal alpha
##report the best alpha
#use more samples to estimate the probabilit\ and Zidth of confidence inter