Note that the page numbers refer to the textbook.

1. (page 26) The textbook gives the wrong answer to exercise 1.4-7 a, although the solutions manual gives the correct value of 1008.

2. (page 34) The solutions manual gives an answer of 1.883 for the conditional probability for problem 1.5-11 (part b). They forgot to multiply by P(B_1)=1/6, so the true answer is .3139.

3. (page 83) In the statement of Theorem 2.7-3, X_x should be X_1.

4. (page 94) In problem 2.8-1 (c), the total cost is C = 3X+(3.5)Y. In calculating E(C) and VAR(C), the textbook and solutions manual both use 3.25 for the cost of beer, and they also fail to account for the covariance between X and Y. The correct answers are E(C)=8.08 and STD(C)=4.593.

5. (page 110) In Exercise 3.1-7, some customer has to wait if the demand for hamburgers exceeds 10. That is, if X is a binomial(15,.6) random variable, we want P(X=11) + P(X=12) + P(X=13) + P(X=14) + P(X=15) = .217277.

6. (page 115) The actual solution to 3.2-2 (c) is sqrt(.8/(.2)^2)=4.472. The solutions manual forgot to square .2 on the bottom.

7. (page 124) For the solution of exercise 3.4-4, the solution manual (page 38) gives "likely intervals" for the observed number of people in each age group. They should not be all centered at 18, but rather at 18, 23, 16, 27, and 16.

8. (page 128) Question 3.5-1 asks for P(X>2), but the textbook answer and the solutions manual both solve P(X>=2).

9. (page 128) For the solution to 3.5-3 (a), the solutions manual writes P(X=0) = e^(-.4) (.1)^0/0! where it should read P(X=0) = e^(-.4) (.4)^0/0!. The number is the same, though.

10. (page 151) In Example 4.3-3, p^(2) should be P^(2).

11. (page 153) In order to preserve the symmetry in the matrix P^4, and make the bottom row add up to 1, in Example 4.3-5, the bottom right-hand entry should be .347 rather than .346.

12. (page 186) In exercise 4.7-3, both the text and the solutions manual calculate the mean time to absorption using the cumulative distribution function F calculated in part a. Of course, this will only give an approximate value. In the text book solution, the probabilities for the function F are rounded off to three decimals, while the the solutions manual the value of F(4) is given to four decimal places (.9221). If you use .9221 you get a mean absorption time of 2.2189, but if you use .922 (as in the text) you get 2.219. The actual absorption time, calculated using the Q matrix is 2.231058096.

13. (page 187) In exercise 4.7-5, both the text and the solutions manual calculate the mean time to absorption using the incorrect value of .3 as the probability of transition from BNP to CNP. The correct value of this transition probability is .7, and the true mean time to absorption is 1.75676.

14. (page 190/191) For the probability histograms, the left hand axis should not be labelled ``Empirical Probability". This is because it is the area of the rectangles, and not their heights, that are equal to the empirical probability.

15. (page 200) The solution (p.413) of Exercise 5.1-5 b is incorrect. The correct answer is e^{-2}=.1353.

16. (page 206) In the lower half of the page, in the formula for G(y), 2nd line: The first 'x' should be an 'X'.

17. (page 209) For question 5.2-1 a both the solutions manual and the text give the answer 2/3 for STD(X). The correct answer is the square root of 2/9. The correct answer for part b is therefore the probability that X lies between zero and (2/3)+(2) sqrt(2/9), which turns out to be .96187269.

18. (page 210) Question 5.2-5 asks you to find the density and distribution function for the random variable Y=2X+3, but the solutions use Y=2X-3.

19. Question 5.2-8. In the solution's manual Y = 1/sqrt(X) should imply X = 1/Y^2, not X = Y^2. Also the pdf should be for y>1 not 0 <= y <= 1.

20. (page 222) Example 5.4-3: In the double integral at the bottom of the page, the y-variable should run from 0 to 1, not 0 to 2.

21. (page 232) The given function f is not a density function. They should have used the constant '2', not the constant '1/2'.

22. (page 235) Question 5.4-9 uses a circle with radius squared equal to 3, but the solutions manual uses a radius of 3.

23. (page 237) On the third last line of this page, F(X) should be F(x).

24. (page 241) The normal curve is centered at mu, not x.

25. (page 249) In the solutions manual, for question 6.2-6 they forgot to take the square root in getting the standard deviation. The actual standard deviation is about 5.39 and the probability is .9681.

26. In the solution for 6.2-9, the final answer is correct, but on the 3rd step of the solution they write P(Z >= (6.21-6.3)/1.6). It should be P(Z>=(6.21-5.3)/1.6)

27. (page 254) In Example 6.3-3, they refer to a Table 6, but they mean Table 5.

28. (page 254) In the solutions manual, for question 6.3-5 part (a) the variance is 2n=14 not 1.

29. (page 259) In problem 6.4-1, the text asks for P(T>1) but the solutions manual solves P(T>180).

30. (page 259) In the solution to 6.4-4, the solutions manual writes (correctly): mu = alpha Gamma(1+1/beta), and in the next step substitutes (wrongly) beta for alpha and vice versa.

31. (page 272) In Theorem 7.1-2 it should be P(Y=y), not P(Y>y).

32. (page 281) In Table 7.3-1, the first two numbers in the u column ought to be .2012 and .8253.

33. (page 292) In equation 7.5-3, that should be i to i, not i to 1.

34. (page 304) In the equation at the top of the page, the term in square brackets is missing a p_S.

35. (page 339) The t-values, called c(n), in Table 8.3-1 are all wrong.

    Update: No, I was wrong. Here's the explanation from the author. "The confidence interval for the mean is based on the "divide by n" formula for variance, not the usual "divide by n - 1". Thus the constants c(n) are not nor should they be values from the t-distribution, but rather they are sqrt[n/(n-1)]*t-values. J. Higgins"
    

36. (page 349) In the solutions manual, for the solution to 9.1-3, wherever they say

    int_0^infinity (1-exp(-t/5))^n dt

    they actually mean

    int_0^infinity [1-(1-exp(-t/5))^n] dt

    There is a similar goof-up in the solution to 9.1-6, and to top it off they forgot to add the constant 12 to E(T). The actual solution is E(T)=11+12=23.

37. (page 367) The solution to exercise 9.4-2 in the solutions manual seems to give an algorithm that reinspects a reworked item until it finally passes. This is in contrast to the description of the system in the exercise and also the diagram (no arrow going from "rework" to "inspection"). The sample output seems suspicious too, given that the theoretical mean is 40 minutes and theoretical standard deviation 14.1539 minutes.

38. (page 391) The solution to exercise 10.3-1 (part a) in the solutions manual correctly gives the solution as P(0<= X <= 11), where X is a Poisson(10) r.v. But numerically they give .2084, while the true answer is .3032.

Special thanks to the following eagle-eyed students: Cory Banack, Jennifer Charters, Justin Gamble, Brenda Hawkins, David Hume, Alan Leung, Tracy McPherson, Paul Shelley, Hai Tran, and unnamed others.

If you know of any other errors, please let me know.

Byron Schmuland

Recent additions from Jayson D. Wilbur at Worcester Polytechnic Institute:

• Problem 3-2.4(a) Solutions manual: E(Y)=0.9, not 0.9011.
• 9.1-4: The solutions to (a) and (b) are reversed in the solutions manual.
• 10.1-2: The stated density does not integrate to 1 unless the 12 is changed to 8.
• 10.1-5: Diagram has 2 short-circuits (i.e., as drawn components 3,4,5,6 do not matter).

Thanks to Andrew Swift for pointing out two new typos! (Feb 21 2005)