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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