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Unformatted text preview: CSBQ4r: Quiz 1A. August 27, 2007. Please ﬁll in your name according to your degree program.
BS in CS BS in ECE All others, (e.g. graduate student) This quiz has four questions (for 40 points). You are to write legibly, show all work and cross out want you do not
want to be graded. References are made to deﬁnitions and methods as used in class and/ or book. If you use additional
assumptions, you have to state your deﬁnitions and assumptions clearly, otherwise they will be taken wrong. This exam is closed book, closed notes, and to be taken without help or assistance. Suspected academic dishonesty will
be reported. ' ' ' Please leave the answers in terms of factorials, permutations, combinations, binomial coeﬁicients,
logarithms, exponentials, summations, products, . . . . . . , whichever is appropriate. GOOD LUCK 1. Suppose you do an experiment in which you ﬁrst roll a yellow die and inspect the result If Y = 1 or
Y = 2, then you roll a green die one time and report the result G, if Y = 3,Y = 4, Y = 5, or Y = 6, then
you roll the green die twice and report the sum of the two rolls, G : G1 + 02. a) (5 points) What is the probability that G = 4 ? Pia=43 :— P16r=4 Si were“ 4‘6» were“ Flﬁ‘igmml‘m
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“’— aca's M :3; M W we m We please turn out or 20 3. (10 points) Consider a noisy communication channel, which transmits zeros and ones, and which receives
zeros, ones, or is uncertain about the reception. Denote the event that a zero is transmitted as ‘To’, that a
one is transmitted as ‘Tl', that a zero is received as ‘Ro’, a one is received as ‘Rl’, and uncertain reception
as ‘Rg’. All these transmissions can be classiﬁed according the following probability table on the left. Thus,
in 30% of the transmissions, a one was transmitted, and a one was received. Find the Probabilities indicated
in the table on the right: P T/RLITO —) or 9165*“?‘5512
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Pia] PM are l' , 4. (10 points) a.) Suppose you have an empty hash table with n 2 90 (empty) slots. What is the probability
that you can insert 9 elements without any collisions? Frabiho W‘g‘m 019% RAW /§é elem] : ith n = 90 slots, where already m = 30 elements are ﬁlled,
and thus only f = 60 remain empty. What is the probability that you can insert an additional 3 elements without collisions? f Prelim WM 50104 Fume [9% WM]?— % jg» 6% 94‘s: EOQ .ml of 20 0339412 Quiz 1B. August 27, 2007. Please ﬁll in your name according to your degree program.
BS in CS BS in EOE All others, (e.g. graduate student) This quiz has four questions (for 40 points). You are to write legibly, sh0w all work and cross out want you do not
want to be graded. References are made to deﬁnitions and methods as used in class and/ or book. If you use additional
assumptions, you have to state your deﬁnitions and assumptions clearly, otherwise they will be taken wrong. This
exam is closed book, closed notes, and to be taken without help or assistance. Suspected academic dishonesty will
be reported. Please leave the answers in terms of factorials, permutations, combinations, binomial COBH‘lCientS, logarithms, exponentials, summations, products, . . . . . . , whichever is appropriate. GOOD LUCK 1. Suppose you do an experiment in which you ﬁrst roll a yellow die and inspect the result (Y). If Y = 1, 2, 3
or Y = 4, then you roll a green die one time and report the result G, if Y = 5 or Y = 6, then you roll the
green die twice and report the sum of the two rolls, G = (3'1 + G2. y??? g .
a) (5 points) What is the probability that G :: 4 ? /7 ’ Flt/£194] : [703:4 / WL Wife1‘ Firm mu] —)—
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36 b) (5 points) What is the probability that Y = 5, given that G : 5? Piles Geri: Eifﬁgerlszresdysﬂyrtw] iéﬁagdté
55f Til/2. 2. a) (5 points) How many distinct 8 letter words can you make if you have 3 A’s and 5 B’s?? gammaCo We :5 waif spasems eve?“ deters/C
P75122014“ F; 71290153wa 36§M§glga4€ﬁxﬁl 90,6:5’ﬂe Mode/Y 5g Lg)” 2. b)(5 points) How many distinct 8 letter words can you ma ' a e 3 A's and 6 B’s?? 7m was «so were 3 WWW“ : 262,532 sv—alaemwrg'£?l+ (i) (“’{Eﬁl§)> please turn 3. (10 points) Consider a noisy communication channel, which transmits zeros and ones, and which receives
zeros, ones, or is uncertain about the reception. Denote the event that a. zero is transmitted as ‘To‘, that a
one is transmitted as ‘Tl’, that a zero is received as ‘Ru’, a one is received as ‘Rl’, and uncertain reception
as ‘Rg'. All these transmissions can be classiﬁed according the following probability table on the left. Thus,
in 30% of the transmissions, a one was transmitted, and a one was received. Find the probabilities indicated in the table on the right: FEE, gr £06 22 17;] 4. (10 points) a.) Suppose you have an empty hash table with n = 80 (empty) slots. What is the probability
that you can insert 8 elements without any collisions? , ‘  p I a
Fri/w (sadism 04% MM? 8 8W17'Mm We.” efw (grease <3
M W9“ (9” 2”” 9&3?” ‘3.. s M for 3% b.) Suppose you have a hash table originally with n 2 80 slots, where already m = 30 elements are ﬁlled,
and thus only f = 50 remain empty. What is the probability that you can insert an additional 3 elements
without collisions? FKTM 00/001‘9‘1’71 05w 1% 6W]: f “g siege/ca W, 4&9 Wm 55‘: EOQ ...
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 The Table, Summation, 3%, e.g. graduate student

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