Probability Exercise #1

Please answer the  following questions:

Description

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.

Questions

Given the first 25 digits of e: 2.718281828459045235360287: 

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

References

This exercise was motivated by Problem 1.2, p. 10, in Introduction to Quantum Mechanics, David J. Griffiths, Prentice Hall, New Jersey, 1995.

Credits

Question by Larry Cain.