This preview shows pages 1–3. Sign up to view the full content.
Problem
I:
(a)
Given
XI
and
X2
are
independent
normal
random variables:

N
(20,22],
Xz
N
(15,
lL),
Find:
6)
E(Y)=
~E(~I)~ECX~L)+~
=
3(20)2(15)+5
=
35
ii
v
(u)
=
327/&1)
t
z2v(x4
$o
q(d)+~
(I)
=
40
(iii)
Probability distribution
of
Y

N
,+c
e
(b)
Suppose
U
V
are norma1 random
variables:
V

N
(20,
32),
Cov
(U,
V)
=
3
L
(i)
Find the
correlation coefticient
p,,
=
bucu,~)

3


;=
Ld.25
5
*
rv
(4x3)
4
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentFill in the blanks in the following:
(a)
If
sample
from
a
population N((20,
22), yield
oi
= 0.2,
then the
sample
size
bj
=

2

%
=
1
*=
fiQ0
JM
r7
(b)
TT
and
ji
(median)
are
taken
as
point
estimators
of population mean
p
then either
E
or
2
or both (which)
are
unbiased
b
0%
(c)
Approximately
9
9
.
74
%
of
the
area
under
a
Gaussian
is included
between
p
f
(d)
Samples
of
size
n
= 36
are
drawn from
an
arbitrary
popuIation.
Then
sample means
E
will
have an approximately
td
OX
n?d
distribution because
of
theCiwJd
L4
#Theorem.
~c
LT)
(e)
What MINITAB
command would you
use
to
generate pseudo
random
numbers with
a
normal
distribution
&
7%
~d
orz?
DR~
4
N
on
L
(f)
The number
arrivals
at a
service
facility
is
a
Poisson
variable.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 n/a

Click to edit the document details