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tutorial7 solution - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1301 PROBABILITYAND STATISTICS I EXANIPLE CLASS 7 Ex.1 If X is the number of heads obtainedinfour tosses of abalanced coin, find the probability distribution of (a) Y=fi (b) Z = (X— 2)2. .L a) A; Xwézn Gag) or 4; 29,57“ (942) 5)}31/23/‘2 a”? W06?“ M oat-L4 ’ 4' I“??? 3 A : 1401‘1‘23/ fill—HT“ , 2 34 ‘flqgfiCqCQVéx/Wzomflf H) 4L 7L I 1069724576 67% h 4‘ “75%;: MA A (q);‘f£o)f‘ 1%) A 3;; ’L" (F J— ‘fflgor i I J— , ’L S [flax] ‘ 56w=€éfléfl fjr/arjr’érg' :.z,;¢fi2c y @406ng J [wais- W 2 (9 I 6.4 Jfi‘flz’éce‘zée‘czfe Mg;éj§ 8 Ex.2 Suppose that X~Beta(2,2), then its pdf is given by fo) = 6x(1 — x), O S x S 1. Find the pdf of Y=X3— 3. ‘(Le 06mm,“ {main mi ‘( A «3 s3 3 ~2 [3 d wrap?) m» 43 jaws 1% s31 :F(><3-3 ‘5) l M 90— (910)5‘ ‘1” ( X S (my) 547 : 1196f? : JQflfiéQ/[l’W/fltk - 2Z5 -} l ’3 a 3 W5. [‘j(y)=é9((/*99-3~[9+3)5 ‘2;— ; My?” / b zicyfifg/zwafjmy‘fi‘ :- wafiwfl) 2269+9’§:/-cm%] 7. Jamil—27 ’6 a 1019ij :2 {Mos-2 - (=0 Wm) b) ér'v/wm) 7: 2* 7W Ex.3 Suppose Z~N(0,1), find the probability of ,1 _{ ,, (a)Y____ZJ:2; X3g :7 I? (fng §(%;’2/1 $337.21" W m fay/d C — - r Y 2 ‘r v A) Y: Z)” (’5 W73 (TM £é€”a¢,0] :: 0/]; “€21: /’%'/ I _ § ’ 0L 6% $0 , 72%? “25” 1 W70 % z—e—C’owj -Z=—fi 3’93, 6) 4mm ’ 69F 11 ' ',o<\ fez/1 01%:1- 5’ % 470.00 bf “Cg ) 5 279 2' ‘ {wk/Wm) ~ -4, 4% J4 J, “finale 23¢ hog-e /2 9 / :Pagg/gu) .1 :fl(‘NSESUj 57"); “I 7 ‘ : @CNJF flip) 2 ‘5"?27529‘6’5flM (ti/vi WW Ekw) Z 7,”?!10) V3?O 2¢?U)+@;gu) “09751—33? Ex.4 LetX bearandom variable with pdf given by a (g: €47?“ ’ {/N),O ' f(x) = (1:304 , 0 < x < 00. (3.) Find the value of c. (b) Find the hazardrate function of X. (e) Let Y = —1nX. Find the pdfon. 3 "9 fl“ Maw C) d! 1W“ m4 / WW f4 c d a ( “,ZLX ) V0(0(<°0,*°4(7(o¢ 0 (K1236? 5: i 3i} (7)2 “in?” [3 W519 0’ [3014031, ‘1 f ‘6’” 0<9C<o¥s %zl M 9(= '9 ,&»~aé<g<a<s 5‘5 p41” vfi ‘r -9 d 1’) fing/x 3 5“ Wk file 2 225/ j; W / } /__e~9 , Z“ I V [+g‘? (F { - WL 36 j ,. .J/j T, .. ’ PM) WW I “(7&3 5670 = 1/ my ...
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tutorial7 solution - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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