tt oj i$l i 7l =jh l-:r -.- fe · o dtxg\= @ +b). etxlyj-- f j ^ jo. e lx'lll, j' r"...
TRANSCRIPT
(h' ? s)r
7-l
b'98 = I ,2 lJ
7 =n t7-x
-(z)? = ,[.*x]gv
- UTEq =fr(t*\V -X?71
s(r+x, =
e l *T: "l ,, g) : [q.(z+n] 3
I Q:n T-<X \aqm ' Xp =np Z+X=n Pl
7-r 7'*F+\, rr-,
;-f = r p(,)le V*l
)f = fr('*x) I
8r T: ar-= vp@Tv ( = vpV)ty r\ =fxlg
b, sfv +y . (x)' (6.U
r\ +((+'r) ,
,) = (t) =j
v
b> x> T-
zj- = fF
ffie t>+l>+7 o (= l>x>0 Jf
t lt r *.,T
+-r : j t7(
l-:r *l fE PJI -.- 7l ;tu iul
tt oJ =JH i$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