Quiz1A1B-Answer - CSBQ4r: Quiz 1A. August 27, 2007. Please...

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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 :_ ‘ ~ ‘ . l- - Préal we Wag 21$] W H: 0mg] + Ptfiizlliw fifteen (L‘s 3 ~?LML W the “61/0266 :— 6 X Z) 1- __ ET; 2. a) (5 points) How many distinct 9 letter words can you make if you have 4 A’s and 5 B’s'i“? l _ 9&4Poér‘fiwmaf‘fdfi swam ,WW WYem‘rngW Me 4' BLWW l ) 370515 is (Z)-l~l:[ ) 2. b)(5 points) How many distinct 9 letter words can you make if you have 4 A’s and 6 B‘s?? I k / 7W Me swammmmr 316’s mm? 685 \b / “’— 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 j‘Ptfo] 2] J (L t l - _._' 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 Wife-1‘ Firm mu] —)— l’f&=4 J You vice] ~ PE You Ema] l ‘ :f, “,6 —,-. 3X§e*gtix%;@ “2&4 Y”;- 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?? gamma-Co We :5 waif spas-ems 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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This note was uploaded on 09/22/2008 for the course CS 394R taught by Professor Vandeliefvoort during the Spring '08 term at University of Missouri-Kansas City .

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Quiz1A1B-Answer - CSBQ4r: Quiz 1A. August 27, 2007. Please...

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