HW4-sol.pdf - Soiution to HW4 5.8 For'11:2 8 111111 31 11.6...

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Unformatted text preview: Soiution to HW4 5.8 For '11. :2: 8 111111 31):: 11.6, We 11111111 (:11 P{X:-.“11=r 11113.113) P1X< :1)-—P{X<: '2 . 11.17117111111111111.1.2311. (1311111 > 3):..1 12(3' 1:111:11 11.1111311:11.511:11. 5.12. 13131111111113 A J with 11 :11 11111111 —1125, we 112111111117 ’ 4} Z2-11.113113. 5.32 (11) I’ruhuhiiily 1.11111. 1111 .1 fire x: 11.131; 1111,1,7:]-- Fl. 2 {11) 13111131111111.)r 1111112111 11111111 2 11111 not 1110 "—' '2': M3310 1 3] :- ff? :r'-(] :13" 3.311 (:1) 11(X .. 11111-1211 :1 :1) 1 #. (h1 17131—114111,“ 31) ....... _'. 5.117 (11.) .131): :3 11311.: '11) z; 1 H1115? 11,112.13. {1.1) .11. 11. (5.11 (11.) T113 1111311111 11111 11111. 111' 2' is 1 “(1.31122 11.11378 which '13 12111301 1.0 1:111: 111111311 111111111 11.6368 1111111 11:: 11.611116. 11112111111131, we (1111111311 :1 11.35. (11) 11111111 ‘. 111110 A11, 2' -= ~~-1.‘21. (c) The 1.111.111 1.111111 1.11 1113 11111. 01' z '13 [1.511111]?11.111138311138118. 1111111011113, 1'1'11111 '1‘111111! 11.3, 3. :- 2.121. (:1) The [11311113111131 1111111111113 111': 1111111 111" [1.1.1135 1.0 1.111.! 11111 01' 1:3 111111 1.1111131'1'11'11 11 1111.111 1111.211 01' [I11231—11.115712121111111 10 1.119 11111 111’ .1. P111111 T211113 11.3, 2 '2': 1.1111. (1.3 (11) ,1 [.17 311),!11 2.17. Ara-11:11 11.111511: 11.113511 {11) z (‘22 -— 3111/11 771.113. A:'(111----1].111118. (1:) z) :2 {112- -- 3111/11 2: {1.33, 2;; =1- [rl'l 311)/[1' :.-: 1.83. A1011 ': [1.96611 (1.6293 :2 11.3371. {11) 3 : 11.8»1. 1110111110111, :2: — 3111111 (61(11811) m 313.114. (3) 21 m ”11.15, 2;) t: 1.15. 'I‘11ca'31'ore,:1:l : 30—1—16167113} :=' 23.1 111111 211;; :.—.- 31]+(16](1.15) : 36.9. 6.111 (11) z -1 (111.1111;9111.111111)/1'1.11:1 2 5 P(X >1 111.1117 ) PM 32.5} 11.111132. "P13331133: 11.11291. 1111' 1111:: 11111.13 1.111.111: 111311.111 11111111011113 (13.31313111111',’ 10.1.1711 1:111. 11:) 3 2111.117 113111111” —1.1, 2-). _{'.-111113- .)111 ).':/11111.—- 1.11; 1931.11? «:11 r: 111(13): P(-— —111 <. Z»: 111) “11181113 111.131: 113321. (c) z ; 1--1..111, :1: 1.: 11 1- [11.1113111111111): 1111;111:1111. 11.111 1311' 1) m 113:; '1” 11:: _- r: 1'1");:-- . .7111 1:11. 1.12711 L111; 1“ 110 1111:: 1111111111121 111 11111:. 11 5113131111 '13 1.1-1 ml 111 11:13 1111111 3 11111111133 T111111 (1 1'11» -. . ._ -)."_ 1117mm ~11 -11....1) {f')(1132111)'.{{1 17211.13 1 (1f)111.1271.) (1111121) 11' *3 1§j( )(11 3211.1" 11.311113. Oti‘rsr “0&1: ) P r STAT 35000-336 21325: Homework 4 PROBLEM 2 Homework problems from the textbook: 5.8, 5.12, 5.32, 5.36, 5.67, 6.6, 6.8, 6.14, 6.45 Extra problems: Problem 1 A satellite system consists of 4 components and can function adequately if at least 2 of the 4 components are in working condition. If each component is, independently, in working condition with probability 0.6, What is the probability that the system functions adequately? Let X: #Quucfl-Congwfi CWKJQNLN‘ZS Mogq % 3km bin%\u\_(‘1\=l£, :Qléb “ tr Li) ale-lease Wile ,«3qgg ’l‘ 'l'lcl‘c) I: ‘3 a Ll, . .1 mace—may -: eta-M — .) ‘3 ”L Problem2 : —— 'ozgé — '153'C3’“: “9108 ~:= [~— binomcdlt g4” B, D = ' 3209 Suppose that a particular personal trait 4 like eye colour or handedness — 1s lass1fied on the basis of one pair of genes. Let d denote a dominant gene and r a recessive. one. A person with do! genes is “purely dorninan ", one with 7'? genes “purely recessive", and one with 1rd genes a “hybrid”. Purely dominant and hybrid individuals are alike in appearance with respect to the trait in question. Children receive one gene from each parent. If, with respect to a particular trait, two hybrid parents have a total of four children, What is the probability that exactly three of the four children have the outward appearance of the dominant gene? Assume that each child is equally likely to inherit either of two genes from each parent. Phanei‘fipe: x=i 5% AijAT)TA \ 3422, ”5 W“ RiXCll“: Pei iA3Am,*rc\} 2 E23]: HER-1L}: Riff} 3 4" \l = is Chechen with {KL-s) ovfi a; a. QLlinivzm my w WWW Q0314, 9:3/43 3 7. _ 23,: Pw‘lClSB‘) : Q3) 6%) Gil):— 425?; ”gill: Jill? :iox‘noMpdfCAr, £1,130 : .1494 ($75 Page20f5 .QZog 7.1:] 1 ‘_‘_'. .2 ' " " “4 4'4” "-3 '2'“ .. _ _ -_ . ._ STAT 35000-SBC 21325: Homework 4. PROBLEM 3 Problem 3- We will ensuine that. the smiling times, in seconds, for an eight—week old baby, follow a. uniform distribution between D and 23 seconds, inclusive. 1. What is the probability that a randomly chosen eight—week old baby smiles between 2 and 18 seconds? .2. Find the 90% percentile for an eight—week old baby’s smiling time. 3. Find the probability that a random eight-week old baby smiles more thanl2 seconds knowing that the baby smiles more than 8 Seconds. Page 3 of 5 STAT 35000-51130 21325: Homework 4 PROBLEM 4 Problem 4 Assume jobs arrive every 15 seconds on average. 1. Specify an appropriate probability model to model the number of jobs arrived during a given minute. 2. What is the probability to get exactly 4 jobs during a given minute? 3. Specify an appropriate probability model to model the waiting time (in minute) for a job to arrive. 4. What is the probability of waiting less than or equal to 30 seconds, i.e .5 min, to. get a job? - . l0 " ‘ ‘ mill Left WK = is? 3:: 8 CxTuhvtfi any fink. ‘ Q3092L Ajgz lt Giuew {Elk}: fit: :4, we “A0; Km Passe-w CR34) if . 9(Stflak\f= eff L Q? K=O ()1) be— if _ if 4 = (00:93“; 53:”: i-IOISZL O l Page 4 of 5 STAT 3.5000HSGC 21325: Homework 4 PROBLEM 5 Problem 5 1. For X N N(,u,02), and z N N(0,1), is Pr ng:P 6““ng5_“? (as ) r( a U) mrmm€(f’flpojb Verify it by choosing a particular pair of (p, a} and some reasonable (1,6. 2. Given X N N(,u, 02 = 9), and Pr(‘X S 4) = 0.6, what; is y? 3. Given X ~ N(,u.:10,02), and Pr(X g 14): 0.6, what is 02? Pr {goéxémo} P{CF\ éZ $073-$849 'R’rL‘méXéHo} Pf H 5 0x0: RrCKQ‘LQ CRUZ” a“ ,‘ ‘2923qflozinowofinCQMQD [f g 0—— O‘Qa — : ..—- T: 9' 78 > (7\ ' “7/933 i,» :9 a?” = ‘ am. 29 II Page 5 of5 ...
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