Errors in the book

Errata for 'Mathematical Foundations of Computer Networking'

My apologies for the following errors in the book.

Chapter 1

• Example 1.15, Page 12: The fact “P(52) = 0.54” is not known at this point in the book. It is derived in Example 1.16.
• Section 1.3.4, Eq. 1.19, Page 20: E[g(C)] should read E[g(X_C)]
• Section 1.3.5, The equation for variance should read V[X] = (Σ x_i²)/n - (Σ (x_i/n))². For practical use of this formula, please refer to this site.
• Section 1.4.1 Note that skewness is defined as M³_μ/(M²_μ)^1/2
• Section 1.5.1, Page 25, last sentence: Variance should be a(1-a)
• Section 1.6.3 Example 1.33, the calculation should read 1-F(6) = 1- 1- e^-6/3 = e^-2 = 13.5%
• Section 1.7.3 Example 1.38 Page 39, the last equation should read 1-p(X=0) + p(X=1)... rather than (1-p(X=0) + p(X=1) ...
• Section 1.8.1, Page 47, the LHS of the last equation on the page should read p(L|R) not p(PLR)
• Exercise 13 should read "Prove ...N(0,1) without using MGFs.

Chapter 2

• Section 2.4.5 Example 2.10 has an error in computation. s² should be 0.243, s should be 0.493, so the t variate is 0.016 (not 0.0048).
• Section 2.4.5 Equation 2.23 has an error: in the denominator, the left hand term's denominator should read n(n-1) and the right hand term's denominator should read m(m-1)
• Section 2.4.6 In equation 2.24, the LHS should read P(o₁^n₁o₂^n₂...o_k^n_k)

Chapter 7

• Section 6.1.2, Page 238-239: The terms “waiting time” can mean different things. In the theorem as well as this proof, it refers to the time waiting in the queue, but not for service. However, the theorem applies to the latter case as well.
• Section 6.2 On pages 240/241, the subscript for X should be k rather than i, to avoid confusion later, where i is used to refer to the state, rather than time step
• Section 6.2.1 Example 6.5: The example should read 'Continuous Space Process'
• Section 6.2.3, Equation 6.2, Page 246: The suffix of the first p in the sum should read “ik” instead of “ij”.
• Section 6.2.8, Theorem 6.11 is actually Theorem 6.1
• Section 6.2.11 ...the probability of staying in the state for m steps is given by p_{jj<.sub>^m-1(1-pjj not pjj<.sub>^m(1-pjj}
• Section 6.3.3, Page 254, first sentence after Equation 6.9: Should read “during a small interval” instead of “during any interval”.
• Equation 6.11, Page 254 “(t)” should be removed from the equation
• Section 6.4, Page 255, last sentence before Equation 6.15: Should read “Given this fact, Equation 6.10, and Equation 6.14, we find that”
• Example 6.22, Page 264, first sentence: Reference should go to Example 6.21, not “6.19”.
• Example 6.23, Page 266, first sentence: Reference should go to Example 6.21, not “6.20”.
• Example 6.25, Page 269, first sentence: Reference should go to Example 6.21, not “Equation 6.21”.

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My thanks to the following readers for taking the time to point out these errors:

• Martin Jacobsson, Communication Research (CoRe), Dept. of IT, Uppsala University, Sweden
• Jinwen Lu, University of Waterloo