answers engineering probability and statistics final 2 drahamdyahmed ahmedawad

10
L4 (') Ao rGl /.t-i c.li,r C," CT: " c;. c'l-= F, n.-t r1 I , 2I ND : o.4 o3t6 = o. OO SEB /z " ts r\ o\ ilzr: 3D n':-{ * ilh",<l- ncfl"r-c<r.^4"[ i r({ hXPer T"nnetri c Ji,hribtnh " '-, :, C: CI-- ^ C,^ :" '3 di\ t (s) :s D ctj C.; Us( \ <)rr r; o. ]=3o n*fonetki*A e( P o.t 3l z?t

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Page 1: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

L4

(') Ao

rGl

/.t-i c.li,r

C," CT: "c;.

c'l-=

F, n.-t r1 I ,

2I ND

: o.4 o3t6

= o. OO SEB

/z " ts

r\ o\

ilzr: 3D

n':-{* ilh",<l- ncfl"r-c<r.^4"[ i

r({hXPer

T"nnetri c Ji,hribtnh " '-,

:, C: CI-- ^

C,^

:"

'3di\

t (s) :s

Dctj

C.;

Us(

\ <)rr

r;

o.

]=3on*fonetki*A

e(

P

o.t3l z?t

Page 2: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

?-\ CL\ x x ),"e fh<rw(y

to ",qhrbt

le*" t(r)Jr *--rQ..t{a*u\*AOsa G(:

r. J arr-x Jn cI exct't) ,1 ,ao

?#rv-r o,,^e.r.\ q bwb tha nQq^

E, (* E{t})r

E((') -(E(*)) '= u'*r (rl

--\ Cpn[i "tq.ll--/

Q)

to[* t I A t ('r\ JtlJ

Jr "3 f*t)

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n(rcr,hton

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\=

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d-- f \ o(v= "-^'(t

Ll'-*, )u,= e-(

*^loo u^ E ., \ u..= e-(€ lo

r.rst tfat\(

t."itfi*t e(-o-ttt =

f r" e-x ,tx

f(r') :

{

et/I*,

ll r

f/r') =

U ?' f'(U. = ?-*

L)tt a ?-.

Ut*ea

(? e -x

0D to

LVac (r'} =

cl'.,, a € *t Jl

(

\trs = e-o

- ZKe-\ - ze x [:lOa o., * e .d Z€-*) -

2 d(,)t = L

( " Le)

Page 3: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

BfJ roto.n^tm(

A B E (x' F(x))'s

r E(K'.,3x't{0-,zK(rar)l(gf-t): E(x3) 33 Ek')t(xJt2E(^) G

-a (€ -'\ Ir f:Til rt=

A "(K)s E(^') eI L =va.r

3t

/^l'-G (*))'

ot

D

Eu ,.. CF1'o- r,.; E (^ * gr^)\'

fo =;r cl:. (q{22

\-\X

-1

+\t

-tt-,)t

2_

Page 4: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

l^/3 -=:

E (* 5al)3

E (K= -. s ,<r.,r) +.2 x G r-1'- Ir :^!)

E(>r) - jE(41(r\ t 26(^) '@r*lL-(rCn)) j

E (^=)4':d'.lto

a+( -z (( -.)\,=.

6

(t -,) *

/3 1

.) b) f =?s

u 3x2 * zx\ - |

( ( r\ ( r ( s:)

V ,IT c heb$hev' s r'n <Ot.<ti g

p( f -Gvk S (S r*s,k) )t \ - 1-k'

f*G'k = lt

a-3 I[- k

-,-"tlAf

3) '-\ vl = tOo

sincr r,\ )3o

Vcr*r (rtl s lt = Stz

l' + 6Yk = s1

= i\ ._+ k =_(,, +".) tr i

I + = t-!= b-BEB1-6.3

T(,r(( (sb) 1t o.t,xts1

0" = ?., El

O E< P'rJ *(S\"tb'<''t;'r

lr=Ju*=5

.p( -o.6e ( z <o.65) = A (0,<t) Q(-o.e/

= O Ger) - t, - o(o.,t)l : a pt:iSil, --, (=

o.sos(

z{s( t -''P tt

F-,) (

2 rt x\ J

Page 5: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

,"\ ;'sl b

p(t) = #"8=-19ztP(otr\ r * y

: o. + t 67

e5

5-- t?.

o- t

P(rrt3, z^JD)

5C ttnrts P (z ) s

P(o\z) : * =

$oX(t)

-5*

tO h6,"rr

+D

:i'O. t

s?q3-Lto

f(s)'3*rb

t liptths

f (o\s) =

* v o't-o, I 6(7

G ,t:) (o sI \)o- zSSt

o. 183?

Eor( s) - D

ro (s)

ost 15 lu lo( pYsb, & bc,-,,et

p(s)P(.:13)

(o 1zs)(o'i:r\)

P(,.r\, "^J D) t P(t:kz t^JD) t

p(r,r 't f(ul ,) r r (z) P(ut,.) +

(o. 4\61 J (o'*J * (o'2\)(o'(66?J t

6,t552Vr.-^ 3

p(s rD) ;

P(D) s

t..' ^ P(uls)(D)

Page 6: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

-lrr(

x$ \(r(t0

[ (r, 1)

r *(**to')I

---- o utL- wF.{

&

= -l t(r,sl J

5

= i* ( * *1.,P= ! L*.,. +. q \:= +[.* * t.z)- (''+"')] = i["**t) -(*.r'*)]

= i 'f J^-;*,)J^-![++(gr"\")]) !,,

= it(+ * r,,)- (+ ; -')J'\[t"')-tt"{= I ("t *.) : c'+g +c' t

q($

t, (-)

S r 5\ y=o) =- f ( y(t.r\ y=")

F (x, t)!, ( x) 1,5

=o) 3 J+(x'1.')6

(Y() P

t(3\ -\

?7J1 'x\vf(1 (r' i, 't,r+0 ' l

Page 7: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

l(Y.(z)P( l't[;o,5,

( x l'l)

2b^ z

\

K lY)-

))1= t({, ly)- (E(Ylfob so

I d [(^ lT) o(x =J x

$$i5

vqf

r(- \ J,v :,,,Q$ + o.t

X2+ o3* rJx =

(

t

J*t

LtCi,;

f-

P ?,-!. 4\f, 15)

r( (x *,g*,) .{r

J^

\tr@' 1

'-t*\

( x?*,)* xJ-\

{ *$ *,) {

I

*a -L[ YsJ--I

\ \-G tJ *.

+)+ +\ :lx3-3

:$ u3

* |/+v)ld3+6

l; (t-Lx\T n ?3tz[+]

'.b *a

IF

Page 8: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

f (r\J)s I x" .f(x lv)J {

-! f (3+ n.j*?g*t- !,

__\-?3*tt

aU*.

Q (x,.J)q,,p

: \ K?)\., tr(J

yr( roy*-,) J*t

\\o.q$+o.t J-

I vt

t5

(

t5

(5,?_

3

+lL,r3J

?\t s,)(

\

+

+

.3

(

\'t

,)

+

t'5-*,5

7

(?

\\t

-\

3s $)Var(rty) s $). (

xl.( x

[(+7_

=3{-

<r-)j

F.(1 ! "lt

Page 9: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

n ,l\ Jrl z Zoo<:t r

l: Iooc

c\

l- 0(r's) =

S/=

?out - \ o

| * o' t'ja1

ZOQ

z { (t ( -''5): A (, (,sJ

: o, c(68Q(-i':\ :

ii) P ( 3o\(* (\to")

\o,o-tog': ( "#2o <:

,- Gq oo\-L 2os )

CJAlG

= ( o, Sjsz) r (t o'(1 r :)

ta

(,

(

P

0

)

)

f(

Q(t s) o C+t

: o- 6z+1

,r) yuo, lr*(, €vf "*"J ro F"i\ te<hx-*^ go.. ( \v'oo

\o. ( x. ( \.dJ x l""t-<lr '4,,'

o 61_q 1 x lsoo s 6e +'7

la^' fs(L\

G,

Page 10: Answers Engineering Probability and Statistics Final 2 Drahamdyahmed Ahmedawad

s) b)

poiso rit,o((.,-, q (n) :

E (x)=

Ji't

€ *+

)x€+*

t+*

xl

Ir

t (tl : 8 x e-8x\

t (6) s Lt e-tE(,

t' ()' 133(

f*\3

4 Cq1fS r... I r^i.r u [*t(+)rry= o,rssr

E g:4rs i -. t*o M i ,a c[c5

t^f : 4 lrx^i,t,-L,,

3 8 la*,o.,i,tr,r-r.y

C (x\ . ,f ; X = T