Q1:

Expected value.

Q2:

print(3 + 2^2 * 4)

Q3:

2 * 0.4^2 + 2 * 0.4 * (1-0.4) + 0 * (1-0.4)^2

Q4:

boardsim <- function(nreps) {
   prbsq7 <- 0
   eb <- 0
   for (i in 1:nreps) {
      start <- sample(0:7,1)
      position <- (start + sample(1:6,1)) %% 8
      bonus <- 0
      if (position == 3) {
         bonus <- sample(1:6,1)
         position <- (position + bonus) %% 8
      }
      if (position == 7) prbsq7 <- prbsq7 + 1
      eb <- eb + bonus
   }
   c(prbsq7,eb) / nreps
}

set.seed(99999)
print(boardsim(1000))

Q5:

egx <- function(xInfo,g) 
{
   tot <- 0
   for (i in 1:ncol(xInfo)) {
      tot <- tot + g(xInfo[1,i]) * xInfo[2,i]
   }
   tot
}

print(egx(rbind(1:6,rep(1/6,6)),function(x) x^2))