Simple Random Walk

RW <- function(n)
{
    x <- sample(c(-1,1),size=n,replace=T)
    rw <- cumsum(x)
    plot(1:n,rw,xlab="N",ylim=c(-3.1*sqrt(n),3.1*sqrt(n)),type="l")
    abline(h=0,lty=2)
}

RWadd <- function(n,color="blue")
{
    x <- sample(c(-1,1),size=n,replace=T)
    rw <- cumsum(x)
    lines(1:n,rw,col=color)
}

RWpos <- function(n,reps,...)
{
Pos <- numeric(reps)
for(i in 1:reps)
    {
    x <- sample(c(-1,1),size=n,replace=T)
    rw <- cumsum(x)
    Pos[i] <- sum(rw > 0)/n
    }
hist(Pos,col="yellow",
     main="Proportion of Time spent in Positive Domain",...)
Pos
}