# Math 3160-003, Spring 2012

## ErrataElementary Probability for Applications, Durrett

Here's a list of the mistakes your fellow students and I have found in the textbook. If you've found another, please let me know.
• Section 2.2
• Example 2.14: The number of trials is stated as 16 in the problem but occasionally written as 10 in the calculations. This means that n-k is 13 and not 7, but the final calculation should still be correct.

• Section 2.7
• #23: The answer in the back for part (a) is wrong. It should be C_(50,8)C_(42,7).
• #29: The answer in the back is wrong. It should be 90/1024.

• Section 3.4
• p. 102: In the second table on the page, all the denominators should be 105. One of them is 104.

• Section 3.5
• #63: The answer in the back is wrong. The answer for (a) should be 3/8 and the answer for (b) should be 4/7.

• Section 5.1
• Example 5.6: Underneath the equation for E(X^2), it says that E(X^2) is infinite when rho is between 1 and 2. It is actually infinite when rho is between 1 and 3 (so while this is true, it is not as informative as we would like).

• Section 5.2
• Example 5.15: The name of the example is misleading. There is, in fact, one median of this distribution, even though there is no solution to P(X<=x) = 1/2.

• Section 5.3
• Example 5.18: s'(x) is said to be 1/(1+x), but it's really 1/(1+x^2). (It's written correctly in the rest of the problem.)

• Section 5.6
• #1: The answer in the back is wrong. It should be 1/9.
• #26: You should compute P(Y<=y) instead of P(Y>=y).
• #29: The answer in the back is wrong. It should be (1-z)^2 for 0<=z<=1 (the factor of 1/2 should not be there).

• Section 6.1
• Example 6.6: There are several mistakes in this example. In the definition of the density function for the gamma distribution, e should be raised to "-lambda x" instead of "-x." This mistake is carried out through the problem: in Theorem 6.1, the powers of e should all contain lambdas. Finally, the conclusion of Theorem 6.1 should be that X+Y=gamma(n+1,lambda) and not gamma(n,lambda).
• Example 6.12: All of the denominators in the table should be 105. One of them is 104.

• Section 6.5
• Example 6.24: When the z-score is discussed on p. 216, an incorrect number is plugged in in the example. The numerator of the fraction should be "99.5-84."

• Section 6.7
• #19: The subscript n in the probability you're supposed to calculate should be 10,000 instead.
• #21: The answer in the back of the book is the probability that the other person will win the bet, not you.
• #41: The answer in the back of the book is very wrong. The expected gain over 100 plays is -\$10, so the probability of a net loss after 100 bets must be >0.5.
• #49: It seems like p=.02 was used instead of p=25/625=.04 to get the answer in the back of the book.
• Several of the answers in the back of the book for problems involving the Central Limit Theorem cannot be obtained using the method of calculation given in the book. For instance, I've checked #31 and #35. The answers are off by anywhere from about .02 to about .0001. If you're doing these problems for practice and your answer is within .02 of the book's answer, you're probably right. You should check to be sure that you're using the histogram correction appropriately, though.