Download - MSO201 IITK assn8 soln
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7/26/2019 MSO201 IITK assn8 soln
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MSO
201a:
Probability
and
Statistics
2OL5-20I6-II
Semester
Assignment-VIII
A. Illustrative
Discussion Problems
1. Let
X:
(Xr,
Xz,
Xs)'
be a
random
vector
with
p.m.f.
f
xr,xr,xr(rr,rr,rr)
:
{
i'
if
(21'
12'rs)
A
|.
0.
otherwise
where
A:
{(7,0,0),
(0,
1,0), (0,0,
1), (1,
i, 1)}
(a)
Are
Xt,Xz,X3
independent?
(b)
Are
Xt,Xz,X3
pairwise
independent?
(c)
Are
Xt
-l
Xz
and
&
independent?
2.
Let
the
r.v.
X:
(Xt,X2)'have
the
joint
p.m.f.
(b)
Find
P(Xr+Xz)2),
P(X?X2>3),
p(Xr:2lXz:1)
and
p(Xt*Xz>
2lXr:
11.
3. Consider
the following
joint
p.m.f.
of r.v. (X,Y):
(
rt*2rz
f
5@r'rz)
:
I
-it-'
tf
r1:
r'2'
12:1'2
(a)
Determine
the
conditional
p.m.f.
of X2
given
Xt:
rr, Tt:
I,2.
f
x,v(r,Y)
aI
r-+
1
2
3
4
4
5
o
08
04
09
11
12
06
09
27
OB
03
05
04
(a)
Find
the conditional
p.m.f.
of
X
given
Y
:
b.
(b)
Find
the
probabilities
p(x
+
y
7),
p(xy
18), P(X
:3V:5)
and
P(Y
:5lX:3).
4.
The
joint
p.d.f.
of
(X,
Y) is given
by
(
.,
fou(r.r.,)
:
J
c(r
-
r
-g),
if
r
> o,a
) o,r*y
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7/26/2019 MSO201 IITK assn8 soln
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(a)
Find
the value
of
the
constant
c;
(b)
Find
the marginal
p.d.f.s
of X
and
Y;
(c)
Find
the conditional
d.f"
of
Y
given
X
:
r, where
r
e
(0,1)
is
a fixecl
constalt;
(d) Find
P({2X
+
3}'
o
ilii,
;?
e
e
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)
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