Set notation in Probability and Regression Review
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I am not sure if this is the right place to mention issues with the book's content itself. If not, feel free to close!
In the Probability Tree section, the footnote is not displaying the latex equation correctly (and I believe union should be intersection):
The set notation \(\cap\) means “union” and refers to two events occurring together.
This seems to occur inside other footnotes too.
Similarly, in the Venn Diagram and Sets section (errors in bold):
Whenever we want to describe a set of events in which either A or B could occur, it is: A∩B. And this is pronounced “A union B,” which means it is the new set that contains every element from A and every element from B. Any element that is in either set A or set B, then, is also in the new union set. And whenever we want to describe a set of events that occurred together—the joint set—it’s A∪B, which is pronounced “A intersect B.”
In the Contingency Tables section, in table 2.4 the table headers describing events B and ~B are mixed up:
| Event labels | Coach is not rehired (B) | Coach is rehired (∼B) | Total |
|---|---|---|---|
| (A)(A) Bowl game | Pr(A,∼B)Pr(A,∼B)=0.1 | Pr(A,B)Pr(A,B)=0.5 | Pr(A)Pr(A)=0.6 |
| (∼A)(∼A) no Bowl game | Pr(∼A,∼B)=0.1Pr(∼A,∼B)=0.1 | Pr(∼A,B)=0.3Pr(∼A,B)=0.3 | Pr(B)=0.4Pr(B)=0.4 |
| Total | Pr(∼B)=0.2Pr(∼B)=0.2 | Pr(B)=0.8Pr(B)=0.8 | 1.0 |
Below equation 2.7 in the same section, the term Pr(A,B) is missing an ending bracket, and equation 2.8 is not tagged correctly.
Hope this is somewhat helpful!
Thank you for the corrections! Much appreciated
Oh also the ~A row total of the contingency table should show ~A rather than B.