> system.time(vec1 <- rnorm(1000000))
user system elapsed
0.200 0.000 0.199
> vec1 = rnorm(1000000)
> system.time(vec1)
user system elapsed
0 0 0
system.time(vec1 <- rnorm(1000))
mean(vec1)
system.time(vec2 = rnorm(1000))
mean(vec2)
x <- c(3,4,NA)
mean(x)
mean(x, na.rm=TRUE)
mean(x, na.rm<-TRUE)
"For Markov chains to be effective the current state has to be dependent on the previous state in some way;"
This is trivially untrue. A sequence of independently and identically distributed (iid) random variables is a Markov chain. An iid sequence is clearly effective at many things (e.g. Monte Carlo integration).
"Not every process has the Markov Property, such as the Lottery, this weeks winning numbers have no dependence to the previous weeks winning numbers." As lambdaphage pointed out, the Lottery does have the Markov property.