A First Look at Rigorous Probability, by Je rey S ...
[Pages:7]Errata for the SECOND EDITION of "A First Look at Rigorous Probability", by Jeffrey S. Rosenthal, World Scientific Publishing Co., 2006.
(Note: throughout, "line -x" means x lines from the bottom.)
Errata to Sixth Printing, 2013:
[With thanks to Julian Ziegler Hunts.]
? Page 181, Exercise 15.2.7: change "a Markov chain" to "an irreducible Markov chain".
? Page 183, Exercise 15.3.3, line 3: change "A0" to "A1".
?
Page
187,
line
-12:
"
1 n
E
should be "E
Y
(n)
sn
Y
(n)
tn
n
n
Y
(n)
sn
Y
(n)
tn
= E (Z1 + . . . + Z sn )(Z1 + . . . + Z tn ) "
n
n
=
1 n
E
(Z1 + . . . + Z sn )(Z1 + . . . + Z tn )
".
?
Page 192, Exercise
15.6.8,
line 2:
change
"
t 0
b
Bs
ds"
to
"
t 0
b
dBs".
Errata to Fifth Printing, 2011 (corrected in Sixth Printing, 2013):
[After teaching from this book again after a five-year break, and also with thanks to Daniel Firka, Julian Ziegler Hunts, Jianlin Zou, Luis Mendo Tom?as, and Sebastiaan Janssens.]
? Page 19, Exercise 2.5.6: change "finite unions" to "finite disjoint unions", and note that P is extended to An by finite additivity.
? Page 20: for clarity, replace "distributions" by "measures" (twice). ? Page 22, line 2: change "finite unions" to "finite disjoint unions". ? Page 25, line 1: "setset" should be "subset". ? Page 35, line 4: "considering" should be "consider". ? Page 36, line 9: missing "}". ? Page 36, several places: omit extra {. . .}, e.g. "{Hn Hn+1}" should be simply "Hn
Hn+1", etc. ? Page 39, Exercise 3.6.5: for clarity, assume F = 2. ? Page 39, line 4: "P" should be "P".
1
? Page 40, Exercise 3.6.11: the notation "" has not yet been introduced, so "Xn Uniform({1, 2, . . . , n})" should be replaced by "P(Xn = i) = 1/n for i = 1, 2, . . . , n".
? Page 40, Exercise 3.6.13: should be moved to LATER (since it uses expectation), e.g. as Exercise 4.5.16. (And "E" should be "E", twice.) It could be replaced by e.g.
Let X1, X2, . . . be defined jointly on some probability space (, F , P ),
with
i=1
i2
P(i
X
<
i + 1)
C
<
for
all
i.
Prove
that
P[Xn
n i.o.] = 0.
? Page 46, statement of Theorem 4.2.2: assume the Xn are non-negative, and then omit "E(X1) > -" (since we haven't yet defined expected values of general random variables).
? Page 46, first line of proof: for greater clarity, replace "(3.1.6)" by "Proposition 3.1.5.(iii)". (Similarly page 107, line 5.)
? Page 46, lines -3 and -2: "E" should be boldface (twice).
? Page 49, exercise 4.3.3(a): change "Z+ and Z-" to "Z+ - Z-".
? Page 54, Exercise 4.5.13(d): replace "E(X) < " by "0 < E(X) < ".
? Page 58, Lemma 5.2.1: note that the converse also holds.
? Page 60: introduce the abbreviations "WLLN" and "SLLN".
? Page 65, Exercise 5.5.9, Hint: specify that y > 0 for the first part, too.
? Page 66, Exercise 5.5.13, Hint: "r different sums" should be "r + 1 different sums".
? Page 71, Exercise 6.3.1 is a repeat of Exercise 4.5.1 (page 52), and should be replaced by e.g.:
Let ? have density x310 ................
................
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