library(dplyr)

n=10000;c=2

samples=function(z){

return(sample(c(1,-1),z,prob=c(1/2,1/2),replace=T))  

}



t=0.5

nt=round(t*n)

v=mean(samples(n)^2)

E_guzai_4=mean(samples(n)^4)

c=1/((v^2)/E_guzai_4)

X_mat=array(0,dim=c(nt,10000))

for(j in 1:ncol(X_mat)){

X=(1/sqrt(n*v))*((samples(nt)))

X[nt]=X[nt]+(n*t-nt)*samples(1)

X_mat[,j]=cumsum(X)

}

S_max=apply(X_mat,2,max)

hist(X_mat[nt,])

hist(S_max)

#t>s

s=0.3

nt1=round(n*t);ns1=round(n*s)

E_result=mean(abs(X_mat[nt1,]-X_mat[ns1,])^4)

3*c*abs(t-s)^2