1. 

None.

2.

g <- function(n,k) {
   sumProbs <- 0
   for (i in 0:n) {
      for (j in 0:n) {
         if (abs(i-j) <= k)
            sumProbs <- sumProbs +
               dbinom(i,n,0.5) * dbinom(j,n,0.5) 
      }
   }
   sumProbs
}
print(g(10,3))  # 0.0.8846817

3.

sk <- function(n,p) {
   mu <- n * p
   sg <- sqrt(n*p*(1-p))
   sumTerms <- 0
   for (i in 0:n) {
      sumTerms <- sumTerms + ((i-mu)/sg)^3 * dbinom(i,n,p)
   }
   sumTerms
}

sk(10,0.3)  # 0.2760262

4.  B has a geometric distribution!

p = P(N <= 10) = 1 - P(N > 10) = 1 - 0.85^10

EB = 1/p   # 1.245135