I
1.1. Consider tbe follorring three randorn experiments:
Experinrent j: Toss a coin.
t/a
u)
Experirnent 2: Toss a die.
Experiment 3: Select a ball at random from an
,hv#'/
urn containing balls nunrbered 0 to 9.
(a) Specif-r the sample space of each experiment.
(b) Fird
e ach outcome
in each of the above experiments
"in,a
Explain \.our ans\\er.
rarge 1:*+^$'=!!gl+retof
number ot rcpetitions ol thc experiment.
fu_
@) sr = { H,T}, n!2= { t, z, 2,4,9 6i ,sj ={o, t,Zr-.- P.q}
T,rofu @in ?n f HJ = f*tTJ =
P;= * v) =t,
Eo, fu- d;r, p.( p = fttz) - . PnE{s-
(q
*
,
*
"
Fo, Arrfrd L",/1, VntoJ --f^crJ - '-'fn[&7 , fnEq =* -#f;
4=
O,. ?
1.4. Anurncontainsthreeclcctronicallylaheledtrallswithlabels(X),01,10.[.isa. l{omcr.and
U) LJoa
Bart are askcd to characlcrize thc random experimcnt that involves sclecting a lrall at ran-
donr and rcading thc label. L,iszr's labcl rcatlcr works Iinc: l{ortrcl"s lahel rcadcr has the
signiticlnr dic.it stuck :rt l; Bart's labe I rcrdcr's lc'i1st siu,nilicrrnt diqit is \tuck al tl.
,646(nrost
.-.2,
' - - 'ia) Wirrt is thc sanrple spacc-cletcrilinccl
by Lisa, Home r, and llart? L9 P
-
Jrir*= (Oc, dt, !-QJ, *oner={ b,tt)
-
c, =fif,ldj
J &yt
alil*ve
cannot occur simulttrncouslv as pairs ol triplcts. and lct /)
"r1
or' /l or C occuls." Show that
bc thc cvcnt
.-.9
l.lt. Lct A. ll. and C bc
lt1t):
n!*t*fra
tri
I'tln) + {Bln) + l',Qt)
Nrcil = N^cd + N, b) + N *cn )
Tb ral'e,o
( fi )r.e
fu/,,,e foun
p-b
{rr,1 -- fpt,t * fic,n fi '* L and
'
of tinle
:.i'i. )-:irra:. that the signal 2 cos2'irt is sampled at random instants
Evert
tat Ftnci the long-term sample mean'
is
events "voltage is positive"l"voltage
lb) Find the long-term relative frequency of the
le's lhan -2."
7V, ca)
4
or1
)
/ou,e
t
I
I
z
M) Sa.ryl* Vo/ar, 4Y< ?il'/ likly *" L" + &.*
+ LonS-torm Ag ,f ,fanyle; = O
C4-) '+'arL '*' vol,u"s ale
P>"b"tle il"rt*
,r4
YnLtl=?^t-t=*
7" CVsaqf p< zJ = 0-+
(b) What arc lhe rclalivc frcqucncics obscrvcd hy I.isa, [lotne r. and
--/lIt
h*f fen
a
J,2r4
jf P,d
J
'l t -3
L)sn, ?OO -Po t''fio= /3 g,# fJorror, *P4 /$' reoJ" *o
hiltereoar'71t Ba rt, b"!! &/, Q I are reoJ au //,/,-ra ?a|= 7,, fro ,4
hcl oI r'c1-rctitions ol the cxpcrintcnt'l
35500
=ffis.
AJeve,,-