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MATH 218 Quiz 3 Solutions

# MATH 218 Quiz 3 Solutions - Math 21 8 Quiz 3 Show Your Work...

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Unformatted text preview: Math 21 8 Quiz 3 . 2/5/09 Show Your Work ' 1. Let X = the number of used cars sold in a day at the Felix Auto Lot on Figueroa. The “Y D We distribution ﬁmction is given below. x! P Pﬁ‘obubth‘i-rj x 0 1 2 3 4 5 6 7 8 9 10 B200 .05 .05 .10 .15 .10 .20 .15 .10 .05 .05 .00 a) FindFX(x). X 0 i Z a L; :3” C; ‘7 ”5 "F (o P «A \ :— Fm .nS’ .w .92 3s #13" .03 «its ‘5’0 ”33 “00 “m x. b) Draw a probability histogram of Px(x) against x. PK (K) 1 '1“ ‘rlﬁﬁ. .lu , u‘f eczea§¢7fcimJ c) Caluclate: P(X27), and P(3SX§6). _ . . PUG?) : :1: t"(><‘/—7) =1*PCK%\ "' l‘ﬁfel L lﬁ‘w'lE 20.2 >3 am .2 are Him taro) ._ 229 .. Piﬁekéél - (90229.329022—2') = Wee) ”(Xe-2) '=V€(©'J“E<(Z)“g‘9lﬂl °" Pﬁékéel '= EC 3) + £02) r £6er (1(a) : .ts“+.lo+ .20 i . '3’ 1 \$032 2. Let T = time it takes your roommate to turn off the alarm clock after it ﬁrst goes off in the morning. The probability density function for this random variable is given by Hi) =30(t“ —t5) forOStS 1. a) If FT(t) is the cumulative distribution ﬁmction, what is FT(1) equal? (Hint: you should not need to compute FT(t).) FT(E\ ‘“ .1. gkﬂﬂi l—(s “he angling WCa-QIMCA oi“ Ocar- ciawsgl—ci ﬂamimn. b) Calculate: P( T = 0.25 ), and P( 0.5 S T S 0.75 ). P(T—, 923*) :2C) swan T ('3 wafi‘h’ki-Nnmfi . .73,— , . - ‘7? ,,— e €(O-(5 é 7740.735) 1 S 30{€‘<ﬂt§]0{€ __ %Q[t§ _:G]) 2 (36¢) ~§£ .5’ C2. '5, .75 __._.f 6' .5” “— .533“? “ .Iocz‘t I «51.92” 5 ﬁft- cL‘L ewétl" fig Li 4. in... (if? ,_. N H RAW! ...
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