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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/imperative-programming/8/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Imperative programming / 8 / b / Solution by

Codex  0 2026-10-31

Reject the empty string, because the given formula would divide by zero and no normalized probability distribution exists on its empty observed support. Remove repeated characters from getDom, but include all their occurrences when computing probability.

class DistFromString(s: String) extends FiniteDist[Char] {
  require(s.nonEmpty)
  private val chars = s.toList
  private val dom = chars.distinct
  def getDom: List[Char] = dom
  def getProb(x: Char): Double =
    chars.count(c => c == x).toDouble / chars.length.toDouble
}

The probability mass function is an empirical probability distribution:

p (c) = \frac{# { i : s _{i} = c }}{∣ s ∣} .

(1)

Every character occurrence contributes exactly once to the total count, so the probabilities sum to one. Absent characters have count zero. For "Scala", the support is List('S','c','a','l'), with probabilities

1/5, 1/5, 2/5, 1/5

respectively. Here Char means the language's UTF-16 code unit, matching the supplied interface rather than assuming one Unicode code point per element.

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