STAT 513 - HW 3 Solution Key

STAT 513 - HW 3 Solution Key - Stat 513 Homework 3...

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Unformatted text preview: Stat 513 Homework 3 Solufions Ex 1.49: I ovary t, Fxfi} g F114 12). Thus we have P(K:>t) nmemgom lmFX{t}31—~FY(§)W1»P(Y§ t}:?{Y>t}. And for some 13; Fxfi) «’2‘: F114;). fir: #3333 11; w: has?» my: Lunam 1w?(th)-:i-Fx{tj >1wF-Y(£)m1mP(Y g.z}m?{Y1>-t}, Ex 1.51: W kind of rand-om van-flame $5 Maxi. hygorgeomeiric in Chapter 3. The firobohmtiwgg obtfinod by Waiting mgumento, as fofiowa. g} ‘5! m 7 WM)” {3 {zoom sing g {fig} 7 mg 2: :2, gm; g; 13%?" H37“) 3: r-oai-gfigofi 13%;: :g " igggx»; 1;. oovowfiw ,4 o f” 1 .4196 6% 9 gm ” am 2 /.(3§)w m5 orgy _ 3 (3X2?) w 4 (23 / (3‘?) g gm .. ’i‘hc tdf i5 3 step {flock-ion with fiumpa at x m {g3 L 3‘ 3, and 4‘ ii :2 Ex 1,552: First, sinceflx) is pdf,f(x) 20 and also by given condition I -F(xg) >0, then g(x) >0, Second, _ W m {(32} d3: M lmFfitB} m }_ {gm-ax * woo” w x0 Thus, from {hose two results, we have g(x) is a pdf. Ex 1.53: 51* ygwwmzwswyammwmyamw<1wzzfimx-am2. mm PVC?) = a is mm. mm. Fm: y a. 1, firw} : 2&3 > e, m E3; is 111m” ‘ Thus for «:11. 2:, FY 33 noadecrmsing. These three feasts vqify that £23; is a cdfi. ' :3) fig: pcifis {Ya} mgfifiy} $31233, {or y 2:» 1, and :2: G, for y f; 1. 3} F33} : m g as} m P{ wry-1) 5 g} w- my g (21mm): FY{(zf13)+3}. Thais, 93(3) w a, {or z 3 a, mi Egg) 3 1 _{1;{{zjm)+1}12), far a > :3. Ex 1.54: a} {gigginxdxmh mum-m 21:31. h) {1; mi: jigxéx+ ;:Ig"xdx : 1 vi- 1 m '2. c :2 1/33. :6! Ex 1.47: henca‘righmntinuaua. '3} is wafinuum gamma a)«-¢i} are mntinamm, us we need an}? {a that}: the limit fifiyfihflt except at {1 what: it is right-cant‘mmm Tb anti me that tins? m nandmeasimg, a} 15:52 %+ «3;.» “3&3 a % + 1%?) m a , Via-4"” _,. ; $.“1....1 law imwg-i-wm {3)w2+=§(~2~)w13 fig; + émhlix” 3w... 3. 13 T as ifi flaming. “at —x WW2: __ wx . (1 <3 :ExE—{z >{L a} fizz: e‘fi a: a, rigging—é ,7, g, 3?, {i} Y{x} w a {at x g; 3’ SQ xfi‘P—m“ A all} m £11 3331;199:1‘”3flx1 ¢ 1. FIX) is flflnsmt, hence Hg" Ufiiflx : Ex ‘2 E}, for x :2- {L ' auras are; wrr‘ect anti ‘35 Fix} a: (i4}wfiw§~—§ 1: G ft): at $ {3, so I? is flaming. 6) 1 ' 7 E - ‘ _ ...
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STAT 513 - HW 3 Solution Key - Stat 513 Homework 3...

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