upstream challenge

upstream_challenge.R

#Challenge:
#Given the following set of numbers {49,8,48,15,47,4,16,23,43,44,42,45,46}. A function picks a random subset of size 6, and takes the minimum, what is the expected value of this function.

#put set of numbers into a container
test.set <- c(49,8,48,15,47,4,16,23,43,44,42,45,46)

#This function picks a random subset of size 6 and takes the minimum
upstream.fxn <- function(test.set) {min(sample(test.set,6));}

#to find the expectation of this function (by simulation) we resample a large number of times:
expectation <- mean(unlist(lapply(1:2000000, function(x) upstream.fxn(test.set))))


> system.time(expectation <- mean(unlist(lapply(1:20000000, function(x) upstream.fxn(test.set)))))
   user  system elapsed 
721.370  11.186 846.715 
> expectation
[1] 8.818875


# the required function will tend towards 8.82 in the long run. 
#i.e the expectation of min(sample(test.set,6)) is approximately 8.82




#alternative method using a loop - which takes considerably longer to run!
aa <- 0
for(it in 1:20000){
	aa[it] <- mean(unlist(lapply(1:it, function(x) upstream.fxn(test.set))))
}

mean(aa)
> mean(aa)
[1] 8.818985

summary(aa)
> summary(aa)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.000   8.768   8.817   8.819   8.867  23.000 
  
  
plot(c(1:20000),aa, type="l")