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Prof. Bjorn Poonen
December 4, 2001
MATH 55 PRACTICE FINAL
Do not write your answers on this sheet.
Instead please write your name, your
student ID, your TA’s name, your section time, “practice,” and all your answers
in your blue books.
IMPORTANT: Write your answers to problems 1–10 on the ﬁrst
page or two of your blue book, without the calculations you did to get the answers.
To guarantee full credit and to qualify for partial credit, you should show your work on
later
pages of the blue book.
Total: 200 pts., 170 minutes.
(1)
For each of (a)(d) below: If the statement is true (always), write TRUE.
Otherwise write FALSE. (Please do not use the abbreviations T and F, since in
handwriting they are sometimes indistiguishable.) No explanations are required in
this problem.
(a) If
f
:
S
→
T
is a function and
A
⊆
B
⊆
S
, then
f
(
B

A
) =
f
(
B
)

f
(
A
).
(b) If
f
and
g
are independent random variables deﬁned on the same sample
space, then the standard deviation
σ
(
f
+
g
) of
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 Spring '08
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 Math

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