f

advertisement
Suppose X and Y are
jointly
distributed rancloni variables with joint density
function
f
c(x+y
)
2
0
:Ox,y1
: otherwise
—
(a) Compute c so that f(x, y) is a valid joint density function.
“
[1
3)
(b) Compute the probability that X + Y> .5.
—I
1
—
2
+-t4)
?(hi
ci
C)
0
43
-
fJ
ill
5.
-
MORE ON NEXT PAGE
7
z
4
—
,/
I
Rt/
_( c1(
ô
-
1)
‘c
4
JJi
3
‘
-
‘i
r’
•:-
D
\
“5jl.r
II
+
X
\jj
1-
\SL1’
:-7•
-p
.ot—
c
S
a)
c_—,
C
.
)-
O/
-:
icr’
I)
%jjçp
s—)
\J’
—
Q
-d
a)
-
ll
CC
Ni
÷
N
4
O
5
__,c__—
>-
><
N
+
z_____
c1
I’
c_
‘%\1r
H
N
eJ
X
-
‘.SjLj-
IL
.ikj
‘-
cj
9th let X denote
If a random customer enters the Smiths Grocery on 8th and
number of
denote
Y
and
er
number of peaches purchased by the custom
Smiths has
the
of
oranges J)urchased by the customer. The management
ing table.
estimated that the joint pmf of X and Y is given by the follow
x
Y
p(x,y)
1
2
0
.2
.25
1
.3
.13
2
.1
.02
the difference between
(a) Use this joint prnf to compute the probability that
s purchased
the number of peaches purchased and the number of orange
1.
to
equai
by a random customer is larger than or
i
(1)2(O))
ô,
)
(b) Compute E(X + Y)
(.z) +
3)
4-
1-
-‘4
(4
4—
I
•
II
c
‘I’
V
r.
CN
I
(-
1!’%
Ir.
‘ft
c_
+
>.q
V
/
I’.
2/
Q5ZQ
Q
:
/
J
5
Ic
5z.o
1)iç&)€
(%)%72
2
c1
—
\--
“4
“4
1
r-
+
‘N
7
c_v
-
-ç
ft
(\
-J
cS
I
L
‘
\\)
cc
%_____
-<
-t
1$
I’
rc,
Sd
>.-‘
c
I’
N
_,‘
c.
‘I
/
U-I
‘I
-1-
c?
,
‘
\-/
cy
J\
-z
c
“
v4
N
f1
oO.
Ir
cV
4
r
scJ,
-
r3
C
“
\
(r
I
r3
(I
‘-‘1
I
I
i-i
$
+
Ii
j2
4I’J’
\-::-1I
II
--
N
-
4
N
41
—s-.j
J%J
—
hJJ
b
‘%f
‘4-
C-r’
--
%J
I)
s
<
ksLc
fK
A
(Th
J1
Il
4
0
11
o1
JDa
p
II .1
25 is random sample of size 25 from a population whose
X
,
1
6. Suppose X
distribution has probability density function:
...,
p(.fX :Ox<
—
0
: otIicrw’ise
(a) What is the approximate distribution of the sample mean
e)
=
0
4
0
.4
MORE ON NEXT PAGE
(b) Compute the approximate probability that
is less than
—
L
1
ç a)
(c) Discuss the validity of the approximation you used in parts (a) and (b).
/
Jot,LU-cf
I
rLL3’
C) r.
i
S
4 44
c:t
1-4.
V
rJ
\pJ
N
c..J
A.
flN
N
It
r.1
2’
rzc
r
k2
,/t(
%or
t&&c
4%
>1
2.33
233)
AJ(o,1
‘A?
)
1;c(
)
?(- 133(
J2(
iL
4
3%
2”
))
133 C,,’) -x
i3(4
%3)
A
x
ii
Ii
I,’
N
N
LI
‘I,
3V
1
L
3CK
N
LA
I
JI
‘U
_t
4
tJ
II
111—
lqL
-t
j)
N
II
h.
‘I
c.
L’
‘S
11
4i
‘4-
rT
4’
A
ii
t4%1
V
rt
I,
‘1
It
‘I
11
-4-
12
1
I—’
p
4
0
I’
H
Ii
—I
U
Lr
NJ
1-
—A
1:
0
1’
V
C
I’
I
II
0
I)
a
Lj
I’
0—
U
1
0
-
I
*
-4
I
‘
0
I
‘L)
Download