(h' ? s)r

7-l

b'98 = I ,2 lJ

7 =n t7-x

-(z)? = ,[.*x]gv

- UTEq =fr(t*\V -X?71

s(r+x, =

e l *T: "l ,, g) : [q.(z+n] 3

I Q:n T-<X \aqm ' Xp =np Z+X=n Pl

7-r 7'*F+\, rr-,

;-f = r p(,)le V*l

)f = fr('*x) I

8r T: ar-= vp@Tv ( = vpV)ty r\ =fxlg

b, sfv +y . (x)' (6.U

r\ +((+'r) ,

,) = (t) =j

v

b> x> T-

zj- = fF

ffie t>+l>+7 o (= l>x>0 Jf

t lt r *.,T

+-r : j t7(

l-:r *l fE PJI -.- 7l ;tu iul

tt oJ =JH i$l =f

7 =f + J=XX=-L arooy? vr$ '

lX=Z t,rantg

(9t*' put) / l..Y=2.yz?zo'yzY,?e l=(6',xt} (t'O

Jasl )Jax'J f,^a. ^av cf vollxlos ), "6pd

4.3 ) {(r'f = g-x o-<,x< 4(a

o) E[fi]= J Vx'fk)dr = A-ot

äama as ilr pa+ Q'

il h) --l o a<ox os,N <27

4: J -

t

{rk)=Ä'Ek)tx

LdSeL

' '

4_ t l f- u o.J.l

D<1L-lU

o s*/z

2 lxl l

r l4-1gquJhret@.

L) P- (r+= ;(üil =J)

. F., 9\ +* o<521

L't J'Ic) Eryr, {, +g)dr = l; 4l S

* L

= P. ( X .y')= J" Q-x ätD

o fvg)=+ \(yl= +Jt.J dJ

,

E L <x<4t6

ElxJ' {

r + & r ) " Tolx=

Ef-x,'J -Va'f txt{ J* 11) B

+)oL

6 \ l2J

=j*F

a'trrx

=)4*JLTL

Vorffl =Ek"l=' - : - ' : '

Vaift3 =

4lT

o dtxg\= @+b). EtxlyJ-- f

J ̂Jo

. E Lx'lll, J' r" s(*!y)dx

= P"td d" : stJo J" t

- va-txl)l = + #J"= B3

s6)

= lrrtJt. = s tJt l

+rY e

3i: dr = _g_J3 J3

E .t) + (x,y) = 2.{ xty 3 O < X.J.1

Find co'',dihon"l lhaon 'o^d

van'cr,nte- o{ X given Y.

Etxl)l; S Ä +kb)dx

. +E)= J: u43 dx = *J'

Page 3

o.J-l

"(+ -fr) # o.r-l

f = FtÄ)l -Et{EL7loxq

"tlJ-3..1lo-TJ

0.J.4{

o.J.4

x'r-3 o <-x' L )

l .ax"dx = 3

dJt

J 4 2 {E)4

2

2/ts 1/ t5 3/s

4/tr a/tr t/r3 3/tr artr +/r

tx) 3/4f, 6/tr a.of tx)

Etxl =

ELx',) =

ZaFh\ = g.t 1f

Z xt{(x) = 33-

z 3EüJ=71{9= *FrY'J =ilT$= *15-

Va.[Ä] = EU'J-fx -. + ^,LYJ= !6. _(Jr= ljJ4f, [/rr zzf

4e,1,

Skg)=EDtyl = LIrg(49 - s 4.\\ r t 15 f f l _ ,

1,

logr 4a7) Ä,, Är. , Xt , X+ i.i.d

F,'"rä n(J), {tb) i{ ) - min tx;J i=t;-t1

R(J) = P- (Ysy)

#,

Fvty) = t- t- [xry)]aRty) = NJ)J T

l - . , 1,, \ -rYy f ;

try 9) -- l-

nb) = 1-

Fx (n'l -- su-x)"drJ: o <x.1

Etxl - too VcTLXJ=/rD Sl[xJ = lO

,l - P- ( min lxr,XTXya) > y)1 - ?'- (xt >J , xlJ , XiJ , xozg)1- {P' tx,>y) ?.Lxz7J)P-trrb) P- U,rry)J

11-?-Lx

L- 2.F

1- J_Q,r)^

= t- (, - (r-u'jtl )to.J <l

O zX -'l

J-VL

{om ftx)={a t 4 -x") o<^c/I o elsew\"re

i. i d

4-

, l-

=?. ( min {p =J)

{r- nU)J t{

dJfv ty | = 4 Lt -F"(y)13 f'[v)

= 'l - Q-ü3

( t- rr0)1(tlt'

{v g) = '12 (,-J)r'S-8) X", Poi ( loo)

P.(/-L"a x^f+Ln) a

f-kr =}s +loo-ldl_:},r =)

Loworßor.,d =-

4- a%üv's Tnz1.

1 2_ 3 {ty)4 t/st 7tt 3/# 6/se

a4st

4/rtz ,/ag 4/st 6/sa

3 3/st 6/st J/st

x) %t loYx ,%t f .o

0.lo) JrA = | '2'3faSeb

, l--Y

4(r,9 )= x9\r

36

)

3Lt1L)r

Z =X7

Vl'z't) = ?

+(Z=1+: {,2,3,4,6, J\ T=lf : {,t,33

= P- (7=x, 1:+)

Y=/ t/st) =ö(1,/ ) -- ?- ( 7: l, T-- t ) = f. (K= t,

g U ,z) = ?- (I.1, T=2) =D

3 ( l, s) : P- (l ='t, Ei)= D

g (2, tl = P- (T=z 1 T=t) - ?(P17=l = h3Qü =P- (r=z rT=2) =P, 0J,'lJ)=4s(

3Qn\ =P-(+J,IJ): D

JG,/) ' P-(+=3 ,T='t\=P-(X*'f=/) =3/s(

Jfr, t) =- P-(TS.T,2\: o

g ß,3) r P. ft=3,T=j)=P-(X- trlJ)=3ft(

f,e resl oll\" p'ob"bi|,{ula,t le(l .fo--Xot'r

colcqlohJn 1

7

T 4 9_ 3 4 6 3 +04 1- i , ,

)362-36

3-3(

Vtt

2

3

2/Et thL ß/st 'l4iL

3/s t %t e/st tw

f(+)n/tL lst 6/st a/st t/tt 9/se1,D

| >a7lY\ > olcn-? ) hT -= (t'rnlY('r-tr) 6l =

7'(t-cn-t6)2 =

lrt ' F-tT ") 6' = (t'r1t) Y

r t- te .ne-l, I t ?fe {el l-

| I -^v rÄv|

. l= | te e^P l=r r J L Tre IGJM_?r=ftr

( frn=r^

lA=/$ Fl ft=Z

7

o7-U-

+>rn € +7> /v\trn-ZT

€s> fÄ

o

,

lTtGztßzo (,ßfq

T 2tR7<Rz rFze

2 =l"l'V it-< (

l.z €ßz r Kz o(rß sß) ? = (€ ß'r\ 6

= (tr,,ßt 6',

(€f,oß rqe

tsllf Nf Jlq

ä = (t)f,T

z$wor n1 fotA+ ll = Z

Jß

7 = pt6'F(ttr'tß, fJß (aR

,0 "j (.ß) 'I (,ßlt i z =

("6i t -- -l.6itt,fi t iu = \"f--,"F,tGi G

fu,o!211' (,tf l pi "il,-l '\.i;.,HX

woSf s"..Y.s1fafy .q& "q

\rL7 .-27k7 tL 11

o1-" o)1/d vl

l-znzo YJ=("):

f o zldwos rc u^*-o6n,

cn. a

| >rtuzQ

a6,ra..rptf{

oJtf=(, l'(r'o)n *Y

(l'oln wo5. : D+l:srss$\s r"puo t;7 rA> rl. (rt'o

.'fllcel (r+zg7 ,OQrgu r zs ßo7 u = \6t7(t +'g;''rJl reuie J3 =törhf(e'hr

"rtVa** pa,ylllll "Tl

e)"1C u^.- - rx Jo s.Jl.z,x \ , xl

;e'e =

[]e -l ,-=u(tr-/ rc- =(rc,e{ x)}

/-x ) zg/1 Y .el-uQ'/ -l =(re',e(r)+

(=g'ro; ol-?.,od cvt' (t,l'ou.,Y{.$ep 4c"'^raeup v suq uM

oT -- -rF( +ty*f = (rt"*g

*ö

oo €- m=u üTan

tD l+t'lt- (r t,-/J \ =

mTvt

(..r t W) -l

(.) *tJ = (.;

?Y

x(r+r€) -

o1'Q' l I

l-z +7 e

vv.7N

(.n) "lJ

"M)tt

uz trl'0orGU _6U

i {")"t: ww 'V. -- ut\A

6 r_-r>-r --LT br

-]

azlnf = cnp

(z\tt

-= (t)1 -37

ar=

lrT- tb

"t +?6

o

f vr'o

)Y f

(t-9t

rn P (r'cn g üol= (r)*

I

t'I

Lt

I