# Esercizio 4.63: i cerini di Banach.
cerini <- 6
tasca <- c("A","B")
fass <- rep(0,(cerini+1))
prove <- 100000

for (i in 1:prove)
{
    nA <- cerini
    nB <- cerini
    repeat {
       out <- sample(tasca,size=1)
       if (out=="A" & nA==0) break
       if (out=="B" & nB==0) break
       if (out == "A") nA <- nA-1 else nB <- nB-1
    }
    n <- nA + nB + 1
    fass[n] <- fass[n] + 1
}

x <- c(0:cerini)
cbind(x,fass,fass/sum(fass))
xm <- sum(x*fass)/sum(fass)
xp <- (2*cerini+1)/sqrt((pi*cerini))-1

cat(xm,xp,"\n")
plot(x,fass,type="h")