Probability Exercise #0

Please answer the  following questions:


Quantum mechanics inherently involves the ideas of probability.  In order to learn and practice the terminology of probability that we will need, let us first look at the following example.


Given the following number containing the first 25 digits: 3.141592653589793238462643, find

  1. the total of all the digits
  2. the probability of finding each of the digits
  3. the most probable digit
  4. the median digit
  5. the expectation value (mean) of the digits
  6. the standard deviation of the distribution.


This exercise is taken from Problem 1.2, p. 10, in Introduction to Quantum Mechanics, David J. Griffiths, Prentice Hall, New Jersey, 1995.


Question rewritten by Larry Cain.