set.seed(68)
s<- c(.25,.35,.5,.6,.75,.85)
u<- qexp(s)
n<-100
data<-rexp(n)
esp_estimer<-sapply(u, function(i){sum(pmin(data,i))/n})

set.seed(68)
m<-50
u<- qexp(.5)
esp_sim <- vector("numeric",m)
for (i in 1:m)
{
  data <- rexp(n)
  esp <- sum(pmin(data,u))/n
  esp_sim[i] <- esp
}
var_y <- sum((esp_sim - mean(esp_sim))^2)/(m-1)
esp_estimer[3]+qnorm(.975) * sqrt(var_y)
esp_estimer[3]-qnorm(.975) * sqrt(var_y)

set.seed(68)
m<-50
u<- qexp(.75)
esp_sim <- vector("numeric",m)
for (i in 1:m)
{
  data <- rexp(n)
  esp <- sum(pmin(data,u))/n
  esp_sim[i] <- esp
}
var_y <- sum((esp_sim - mean(esp_sim))^2)/(m-1)
esp_estimer[5]+qnorm(.975) * sqrt(var_y)
esp_estimer[5]-qnorm(.975) * sqrt(var_y)


s<- c(.25,.35,.5,.6,.75,.85)
u<- qexp(s)
fun1<- function(x){x*exp(-x)}
fun2<- function(x){exp(-x)}
sapply (u, function(u) {integrate(fun1,lower = 0,upper = u)$ value + u* integrate(fun2,lower = u,upper = 10000)$value})