SolutionsSum04

SolutionsSum04 - FINAL EXAM - STATISTICS 241f51 July 2004...

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Unformatted text preview: FINAL EXAM - STATISTICS 241f51 July 2004 Time: 1.5 hours Student Name (Please print): .............................................................................. .. Student Number: ................... ................................ .. STAT 241 STAT 251 {check one) Notes: a Total points equal 100. 0 Show the work leading to your solutions in the space provided. Indicate clearly the part of the problem to which the work relates. a This is a closed book exam. A single 8r1 / 2 x 11 page of notes (2—sided) is allowed. a Clean statistical tables from the course notes are allowed. a Hand calculators are permitted. Problem 1: Let X be a. continuous random variable with density function f(x)=1—::—$‘ forug 1:39. (1) 1. Determine a . 2. Calculate P(X > 5) 3. Calculate P(X > 3 '5 X < 5). :1. Suppose X1. X2, ..., X 20 are independent random variables with common density function Calcu— late the median of Y 3:- min {.Yh X2, ...‘ X20}. Answer to Problem 1 m I. Hoodx: 7—995. g. -90 0 g L‘fndx e- e ..__’:_. gum; film use—Lav ' m Answer to Problem 1 (continued) E13 Problem 2: The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean u - the actual temperature of the medium- and standard deviation 0. (a) For what value of a. 95% of all the temperature readings are within 0.100f a? (b) Suppose now that a = 0.05”. For what value of n... 95% of all the averages of n independent temperature readings are within 0.01“ of p? Answer to Problem 2 a. )(Nmyf) H [II-0.19:5 p4+o.|)=0.‘15 [a] “'9 Pl $Js§£<£¥Plfl<2éfl I3] Answer to Problem 2 (continued) [2] C63 is]. Problem 3: 30 lots containing 20 items each are randomly chosen. All the items in the lots are inspected to estimate the unknown proportion p of defective items. 1. Let X,- (t' = 1. 2. 30) be the (random) number of defective items in each of the inspected lots. What are the expected value and variance. for the total number of defective items 53x¥1+X2+"'-L;x'30 I." 2. Suppose that the total number of defective items found in the 30 lots is 150. “that is your estimate for p ? 3. What is the approximate probability that this estimate differs from the unknown “true” proportion of defective items p by less than 0.02? Answer to Problem 3 '- X; ~ Binor'fial (7.0,?) EX =- hP= 20 P E 2.? Vary mph-pawn?) L z] 30 S = 2 X: 'i-‘I Els)-- H iXi)‘30EXa-= 6oof> cs] YarfS)= Kurt X: ) =.-_ 3oUMXUa 600,90?) C i] Answer to Problem 3 (continued) “‘— ~N(o.l) My CLT) E12 3(2) ti] : P("'I.BI €85. N3! ) =Q74'g IQ l.l3l)==o. 97015) L_ Problem 42 A drunkard executes a “random walk" in the following way: each minute he takes a single step North with probability 2/5 or South with probability 3/ 5. The directions of his successive steps are independent and their length are random variables with uniform distribution on the interval [20, 60) cm. The length of each step is independent from the direction he is walking. What is the approximate probability that the drunkard will be at least 1 meter away from his original location after one hour? Answer to Problem 4 Ai=i+l “I 60 S = 1' MB. 30‘“ Ba ~ unef (20,60) E BIS): L— - "'- Bo'-E(43)ECB3) ~= 600%)40 :42» Var“): Vat igAiBi) -'=' so VarMiBi) Answer to Problem 4 (continued) 37 0” .I' «v m erg), VarC$»=M(4<PO, {00:50) 1:31 P( lSlzloo)-=P( Sawo) +P($g-loo) :P( 3'48!) s 'lw'flb) \l '00'60 J Ivouso +P( 3-48" ‘2' [00-480) W“ 17.55 =— 0.1!83 [‘1 ...
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This note was uploaded on 09/07/2011 for the course STAT 241 taught by Professor Kanters during the Spring '08 term at UBC.

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SolutionsSum04 - FINAL EXAM - STATISTICS 241f51 July 2004...

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