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Lecture 9

Lecture 9 - Continuous random variables Example Height...

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Unformatted text preview: Continuous random variables Example: Height measurement- how exact can you get? interval size=5 inlerVal size=1 a: O O to O o E Q 2‘ v 5' a g a B 3 Q N D N c j g 8 E O 1"'—“"'_""T_‘_"—“'—T'"_—"_—"l ‘3 I—r—r——-—r—-—r-'—-r———i—-—'i 50 50 70 so so 55 so 65 TD 75 so 35 height height I! O D _. 8 8 ,, o ‘3 r: g .2: 5 ., m '0 E E" 3 3 a E) E N O D 8 8 D O . ‘ so 55 so 55 7a 75 so as 50 55 so 55 7o 75 so 35 height neigm More examples: weight, waiting time till an event, Probability E Area under a curve Probability of measurement being in interval (a, b) = area under curve from a to b. P(60 < height < 70) 2 area of shaded region 006 uensuy 0.04 0.02 0.00 f“ I: a Ox QQn +00 be -) ( b r cl? {-m )dx 0\ a]: (I : Hm iguanhanxk ma! AXK‘)‘ ‘ ( Ru'emmn Sum ) 00 = j ghdftx) ab: BOCcuASQ PanevHoS 0f MPQcTu?|'oﬁ Sud. as — addﬁiuf‘ly .— ‘;GQO(;'.'7 of! , \noN for 4(5me WV. 5 , ﬁne Pnrpe'rhIS mmsf (mh‘nme {b hdd “for Cm‘h‘nuoms (Al-S. Shnﬂour‘, folr Pwpkri'h'iof- VONCX.) ON) 3000 Sa‘nq 13959 are deﬁned “mask Qxyed‘ad‘l‘o‘a . Ye’r anonr way 1!» Manama ﬁe (dnLQP‘r 0“ k den\$l:bf ’ QPPI\’L0\‘J'Q +5 muifi-d;men3§ono~l V‘. V. X For any 3mm” (onaedgg neigborkomi A P( x e A) E {(xo).(s;3¢ of A) wkue an, (5 any P05“ in A . LA 5.“ 013m . 1: +113] In 2—0UM +05.) 3‘9. 51(X‘IX‘) is A r. dedor Formally : Property of 0- dQﬂSI?" {KﬂCfg‘aﬂ /- {'(X’ 20 far all I 6 (-00) as) P(& E. X S L) :: J: ft1)c[x Deﬁne Flat) = P(x 5 x) f3 be He (CDF) 5x3. We say X N Qﬁpontnﬁax‘ ()5) [-M. X has Cm exponenHal 0‘;S+r:bv~ﬁoa wﬂ’ﬁ gaomma‘tor ) ] The QXPOQOni'iOL‘ 1““.- Ca (‘13:! No 3&5 h‘meg P(X>x3={€- I )3: - ‘F x20 3(- x<o :f x 3-0 1" 1‘0 IF )(>o the [S a good moale,| for I Q‘ﬁ“ ‘h‘me {Tam one ru&.ag‘h’~ae decay ﬂuent? +1) “"8 nPXf. (032 i : Y 3 g (X) (a. F) I‘S \‘n meaSu‘tj To 1*” fylg) , 7 Swan“ 1—C\kQ O. Sing” "JN‘H’J (3-1 ) ‘31.) Ground ~1_ FPM‘ we Lawre\$Ponol.'/L5 LYI)XL) aromol X. 0-9. solue §(x)=‘3 far or %(1\)=’3‘ hf I. P( ‘(6 (an, 31))=P(xe (an); ‘6‘](3) (\$173.); fXCX)-Q&-xl) -f follows KW? _' _l Ll). Ty”) = fx(3(‘a3)§%§(u) 2). 15m: [hm-Jr] -. FC‘) {5 °~ 31";6‘47 \‘ncreasCAg ”M. (an Fm: Nye a) ) wﬁ-k mam-um {0). Q1 H003 Cow we genorgL (Sample) a UOt‘N for Y ﬁu‘uen ﬁnk we “MI“! 0 UW'H'OIM (‘mndmn num‘Hr‘ ﬁenetadov'? Sch-dim I The \JmC-(n randm num. generd» ﬁenewd‘bs X «2 Wm'f [0, I] . 11’— we Seﬁ' Y: F“(x) \o senerw’re Y 'V F(" ﬁen 33‘ Y: F4”) 6%. 50hr? F‘Y) : X I“ e"? :2 3C #0:? " -)\3 :: ﬁn (l'x) ‘3 t: -"!>": can (PX) Le. Y=-'%:£"("X) bun“ have (A ex? ()3 d131- Hm: Skew ”\{S :33" pH)" \ y: @(X) ) gf.) {s Smoo‘l'k and mend-one What {f 3%) JCtmasﬁng ? : ﬁdexp fxuc) (- 3—35. {S LI‘RPCAf +(nn5‘l'ufm N'fx'On : 1" Y: GLX+L where air—o Y -- b & ﬁQn X = 150m {us-2:9». 1%] I ﬁ(‘g-L) CL 0 use Smyfose Y: ﬁ-X u: .-.: "Y K” {3‘3}: ke—lé u+3>o 'e =J‘X Cs axptx) ...
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