ECE 434

Fall 2002

A List of Errors and Misprints in the Text by Stark and Woods, 3rd Edition

The following is a modified version of the list of errors found in the 2nd edition of the Stark and Woods text. This list includes only those errors present in the 3rd edition of the text. Throughout, TEX notation has been used.

• [page 29] In the third line of text above Eq. 1.8-7: "particles among in cells...": "in" should be "n".

• [page 43] In item 2, there should be a space between "k" and "(k>1)".

• [page 63] Equation in middle of page: It might be clearer to include an intersection symbol in equation {X < x_1}{x_1 < X < x_2} = \phi

• [page 123] Item (i): last complete event at end of the first line should be {x: x<0}.

• [page 149] First line: "m>=n" should be replaced by "m<=n".

• [page 190] In the 4th line above Example 4.2-6, you should replace E[Y|X(\eta)] by E[Y|X=X(\eta)] since the terminology E[Y|X(\eta)] has not been defined. It might be helpful to add a sentence like the following: "If we define the real-valued function g(z) = E[Y|X=z] then we can formally define the {\it conditional expectation of Y given X} as the random variable E[Y|X] \eqdef g(X)."

• [page 223] Third equation in Example 4.7-7, second line: "-jw_2x" should be "-2jw_2x".

• [page 228] In the Taylor series expansion of \ln{\Phi_{Z_n}(\omega)} there should be a factor of 1/2 in front of the quadratic term and a 1/3 in front of the cubic.

• [page 278] In the 1st equation of Ex 5.7-1, the w_1, w_2, and w_3 characters should not be in boldface in the exponent. In next equation, same problem with w_1, etc on the vertical bar following the partial derivative.

• [page 397] Problem 6.36 (b) (ii): In the expression "X[n,zeta]", the zeta is bold-faced and should not be.

• [page 419] In computing E[X_T^2 (nT)] change ns^2 to (n+1)s^2. Two lines later change t\frac{s^2}{T} to (\lfloor\frac{t}{T}\rfloor +1)s^2 .

• [page 439] In item 1, it says "which directly follows from E[|X(t+\tau) -X(t)|^2] \geq 0 . For complex valued X(t) this leads to Re[R_{XX}(\tau) \leq R_{XX}(0) which does not prove the result. Instead use the Cauchy-Schwarz inequality to get |E[X(t+\tau)X(t)^*]| \leq \sqrt{E|X(t+\tau)|^2 E|X(t)^*|^2} = R_{XX}(0).

• [page 488] The "only if" part of the proof of Theorem 8.1-1 is omitted. Here's a correct proof. Suppose the process is m.s. continuous at 0, we show that R is continuous in a neighborhood of (0,0). Note that X_tX_s-X_0X_0=(X_s-X_0)(X_t-X_0)+X_0(X_t-X_0)+(X_s-X_0)X_O Take expectations of each side and use the Schwartz inequality to find: |R(t,s)-R(0,0)| \leq ||X_s-X_0)||||(X_t-X_0)|| +||X_0||||(X_t-X_0)||+||(X_s-X_0)||||X_O|| where ||Z||=E[Z^2]^{1/2}. The RHS tends to zero as (s,t) converges to (0,0). It clearly follows from the same type of proof that R is continuous at (t,t). QED

• [page 515] "I" should be replaced with "1" in equation at the bottom of the page.

• [page 521] The 2nd and 3rd lines from the top are identical equations. Remove one.

• [page 555] Equation for a_{io} at the bottom of the page: "a_{io}" should be "a_i".

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