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• Longest runs in coin tossing. Teaching recursive formulae, asymptotic theorems and computer simulations

  261-274

  Zsolt Karácsony

  Józsefné Libor

  Views:

  33

  The coin tossing experiment is studied, focusing on higher education. The length of the longest head run can be studied by asymptotic theorems ([3]), by recursive formulae ([10]) or by computer simulations . In this work we make a comparative analysis of recursive formulas, asymptotic results and Monte Carlo simulation for education. We compare the distribution of the longest head run and that of the longest run (i.e. the longest pure heads or pure tails) studying fair coin events. We present a method that helps to understand the concepts and techniques mentioned in the title, which can be a useful didactic tool for colleagues teaching in higher education.

• The sum of the same powers of the first n positive integers and the Bernoulli numbers

  91-105

  István Molnár

  Views:

  28

  The first part of this paper presents a method to calculate the sum of the same powers of the first n positive integers which is non-recursive and easy to express algorithmically. The application is demonstrated through several problems, for example by calculating the sum of arithmetic progression of degree p. The second part of the paper shows that the discussed procedure can also be used to calculate the Bernoulli numbers, and then, with the help of a known theorem, a link is established between the sum of the same powers of the first n positive integers and the Bernoulli numbers.