The book by E. A. Jackson has a nice introductory chapter on probability distributions.  Here are two problems from this chapter:

1. Jackson p. 28 # 11
2. Jackson p. 28 # 13

You will certainly want to read pp. 28-33 about the uncertainty or Boltzmann entropy of a distribution.  A related exercise is:

3. Kittel p. 57 # 12.2

Also do:

4. Kittel p. 57 #12.3
 

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