CS208 R Solutions

PP_pr.R

# q1
pi_D <- function(n, P) {
  if(length(P) != n) {
    stop("Number of probablities should be same as n")
  }
  else {
    # return an element from {1,2,3,...n} with probability P
    elem = sample(1:n, 1, TRUE, P)
    return(elem)
  }
}

# print(pi_D(4, P))

#q2
pi_WS <- function(n, r) {
  if (n%%1 != 0) {
    stop("n has to be an integer")
  }
  if ((r < 1) || (r > n)) {
    stop("Condition for r: 1 <= r <= n")
  }
  
  P = vector()
  # initialise all probabilities to 1/n
  for (p_i in c(1:n)) {
    P = c(P, 1/n)
  }
  
  # maintain count
  s = 0
  output = vector()
  
  while(TRUE) {
    # print(output)
    if (length(output)) {
      if (length(unique(output)) == r)
        break;
    }
    x_i = pi_D(n, P)
    output = c(output, x_i)
    s = s+1
  }
  return(s)
}
# print(pi_WS(5, 3))

# q3
pi_B <- function(n, p) {
  return(rbinom(1, n, p))
}
# n = 29
# p = 1/5
# print(pi_B(n,p))