{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW5_Solutions

# HW5_Solutions - NDU-BE-EE’IBS 16 44 ‘ F Ell[213_t...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: NDU-BE-EE’IBS 16: 44 ‘ F' . Ell/[213 _t x—I.5 ‘ 40. (a) f(x)=ﬁ;1(2)e 5[ '1 J P[1.1 {X4 1.91213 141-1-5 { X-1.5 {1.2-1.5 3 .2 .2 = H2 3: z c 2] = 13(2) — 1302) = .9772 ~ .0228 = .9344 (b) I_='[X 4.91:2[X‘21'5 {'9‘21'5]2 P[Z «c: -3] = .0013 24—215 3 2—1.5] 2 P[Zl‘* 251:1-.9933 = .0062 This small probability is indicative of an unlikely extant. (0) yes, P[X :3 2] = P[ ((1) Need to ﬁnd x0 such that PIX 2 203] w .10. PREK01=P[ZExn—'2L5]=.IO .23} x031‘5=3m=1*28 r.» xu :1.5+(1.28)(.2)=1.756 g/cnf 44. (a) no, P[X 3 1375] = 012 5 .17] = .4323 (b) P[X '4 1070] = P[Z :4 .33] a .3707 62. E[X2] = 13.223.44.443. = jaﬁxt+‘e-m‘dx 0 0 )2 Hr“ Let 2: = am”. This implies that x = [E] and :12; = L?) dz Substituting, it can be Seen that =4 24”“ 1 24-1 .. 24 i 4—3 we) [X] MK“) e 4.4[4 .4 e = a_%:b[z%e"dz = a“%F[l+%] 65. (a) .9974; .96 (b) .8812 (c) .9996 (d) .8988 (e) TH: .9964. V: 999999; .9537 NDU-BE-EE’IBS 16: 44 (at) NU} - flail mam 1 umupuucm ta uycmmc] '3' [32/213 = 1 — P[nonc are operable] =1—(1«w.9)3 = .999 (b) R5(t) = P[at least 2 components are operable] = P[2 are operable or all 3 are operable] = [3(9): (1—.9)+(.9)3 = .972 OR R50.) = 1 — P[none or 1 is operable] = 1 — [.001+[31'](.9)(.1)2]=.972 (9) Mt) = (.9)3 = .729 ‘72. y:e":¢.~x=g"(y)=]ny andx302>lnysﬂorype°=1 on 1 no _] _x 76. (a) Since PM): [acme—ﬂit, 1"[-2v]= Ix As six, 2:930 Q 0 3 . 1 . . (b) Let x =% such that dx = tdt. Substituting mm 115] In 76 (a) ylelds m _% '1 an _,, r1 1‘ [—1—] = iii] e_{ ﬂair = Hit—He ML]: 2' O 2 I] an 1 _(l%) [1 J _ f. = 2 —-e a: = NE w — Jr J; J J1} 2 I (2164):!!! =1 and the standard normal density is symmetric about 0) (since “ti—2;- NDU—E’E—EE’IE’IS 16: 44 C = . + X - UMJ') mufﬂer} J \W) =_1H[ I {My 1 E—a-ar] 35 J57? ‘ «Er? _ 1 1 -%J‘ 1 44%” ___.g.___ =_w__ 2‘5 ﬁg 2541(1))! a 2 . 1 (d) f,’ (y) is the dents-ﬁt}r of a gamma random variable With a = “L; and ,6 = 2. A chi-squared random variable with 31 degrees of freedom is a gamma random variable with a = gand ﬂ = 2. Thus, y =1. 78.322222-1 z; [51: 13211. 2:20 :3» z: 31—“ and d321, _2... . i] 2 4 y+1 3::0 => 2':-— y_+_[ and dz=—l _._,.2__‘ 2 4 y+l (H m 1.2”: 1 ﬁve) J5 “—2 24y+1ﬁ 432+] -1. + = 1 24b”), y‘p—l 4 :rr(y+l) 1 Jim) 1 _}/ -l(y+1) f J“ =2'hl J’ =~—"-'"—€‘ = y+1 33" 2 F' . [EB/[33 TEITFIL F' . E13 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

HW5_Solutions - NDU-BE-EE’IBS 16 44 ‘ F Ell[213_t...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online