Math
351
W.T.
Kiley
Clearly
show
your
work
and answers.
Follow
the
Honor
Code.
\10)
t
X
is normal
with
a
mean
of
10 and
a
variance
of
25. Find:
a)
the
probability that
X
is
between
7
and
13;
Exam2
December
2h
2009
b)
an
interval
that
has .92
probability
of containing X.
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;r7;'?=l{)
=
r
(,
6
{
z€'
o)
='7
e
5
7'
A4743
=
''
?s/4
b),
q
),=
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<
2
4
0/,f
.',
.1
6
=
PI
As
"7,
)
"
/wt
=
/,75
.n,
t[,zf=
tX
to)/f
^.
(
X
;
/0t
tr,7,f
07)Z
Y
is
the
mean
of
36 independent values
of
the
above
X.
Answer
the
same
2
questioas
about
Y.
"'
E(f)
=
10
)
Va+
0)=
]Eb6
;
7
=
(rrD/(
%)
^)P0<Y<tz)=
l:r,!,:
z:,t,:)
:n
7z6#{#
l)
tl.zs:
(ttd/tA',
/=/atl,qrg
t,
O)t
The p.d
f
of
X
is
(*):
lxl
for
1
<
x
<
1.
Find
the
p
d.f.
for:
a)
Y:
X^3;b)
Y:XnZ
.
",
f,
d
?r;
6;1
t:#;{
r'
/
4":
}
o
R
ry
$\
=
F(x'r
g)
=
\!,"'
1.il
h
;
I
T
l"
{rtp

Fi
)
Fytp
=
r(x
Ar{,,il,
F;
tr)
Z3
7
$)=
le*l
b
ir'"
=
qlr'llt
,ril;6t
*Fn
L=
u't6
nt*
It,2
S,
t
8,1
5J
ftr,
s
fi,il.1sl
i,hl/*
/
,/,t,
0
(
7
.l,