1.  generic

2.  

ET = E(X1 X2) = EX1 EX2 by independence.

EX1 = (1/3) 69 + (1/3) 72 + (1/3) 70 = 70.33

ET = 70.33^2

3.  

sim <- function(n,nreps) {
   w <- replicate(nreps, {
      x <- rexp(n,1/2)
      xbar <- mean(x)
      abs(xbar - 2.0)
      })
   mean(w)
}

print(sim(1000,10000))  # 0.05

4.  

kNear <- function(x,y,k,newx)  # x,y are vector, newx a "scalar"
{  
   dsts <- abs(x - newx)
   odsts <- order(dsts)[1:k]  # which are the k closest?
   mean(y[odsts])
}

x <- c(5,12,13,8.88)
y <- c(22,11,5.5,12.12)
newx <- 13.2
print(kNear(x,y,3,newx))  # 9.54