Midterm Exam 1
CS70 Blum/Wagner, 9 March 2001
This is a CLOSED BOOK examination. One page of notes is permitted. Calculators are permitted. Do all your
work on the pages of this examination. Give reasons for all your answers.
Problem 1 (Short answer grabbag)
[10 Points]
For parts (a)(c), justify your answer briefly.
(a) [2 Points] True or False: (P => Q) => (Q => P) always holds, for all propositions P, Q.
(b) [3 Points] True or False: ((P v Q) => Q) => (Q => (P v Q)) always holds, for all propositions P, Q.
(c) [3 Points] Recall that two sest S,T are said to be
disjoint
if
= Ø. Can two events A and B be
simultaneously independent and disjoint?
(d) [2 Points] Recall that two random variables X and Y are
independent
just if the pair of events X=
i
and Y=
j
are independent no matter how you choose the values
i
and
j
. Which of the following most accurately
expresses the proposition that X and Y are
not
independent? (You do not need to justify your answer.)
Problem 2 (Permutations)
[25 Points]
Let
S
be the sample space of all permutations on the
n
letters {1,2,...,
n
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 Spring '08
 PAPADIMITROU
 uniform probability distribution, Eta Kappa Nu

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