#--- Gift Accepting Problem ---
  



hist(rnorm(1000,100,10))




y=100
lambda = 1
c = 5

q = 1-pnorm(y,100,10)

X = rnorm(5000,100,10)

(X-y)

((X-y)>0)

((X-y)>0)*(X-y)


mean(((X-y)>0)*(X-y))




#--- Find optimal y ---

for (i in 70:130) {
  y=i 
  X = rnorm(5000,100,10)
  print(  c(i, mean(((X-y)>0)*(X-y)))   )
}





#--- Simulate Gift Accept/Reject ---

y = 98

X=rnorm(5000,100,10)  # 5000 Gifts
T=rexp(5000,1)       # 5000 interarrival time of gifts


acc = which(X>y)[1]   # order of accepted gift
acc
sum(T[1:acc])         # time of acceptance
Cost = c*T            # Cost of waiting
X[acc]                # value of accepted gift


#- put them in loop

y=98

c=5
lambda=1

T = 0
Cost = 0
Val = 0
for (i in 1:10000){

  X=rnorm(5000,100,10)  # 5000 Gifts
  T=rexp(5000,lambda)        # 5000 interarrival time of gifts

  acc    = which(X>y)[1]   # order of accepted gift
  T[i]   = sum(T[1:acc])   # time of acceptance 
  Cost[i] = c*T[i]            # Cost of waiting
  Val[i] = X[acc]          # value of accepted gift

}

Ret = Val - Cost


hist(Ret)
mean(Ret)
sd(Ret)








#---

T = rexp(100,5)
plot(cumsum(T))