1.
[14
points]
A
message
source
that
produces
a
sequence
of
4
bits
of
information
is
equally
likely
to
be
in
one
of
three
states:
5,
Si,
and
Ss;.
In.state
Sk,
the
4
bit
sequernce
can
have
at
most
£
1's,
with
all
such
4
bit
sequences
being
equally
likely.
For
example,
in
state
Sy,
the
source
can
produce
the
sequences
0000,
1000,
0100,
0010,
0001
with
each
of
sequences
being
produced
with
probability
%
Let
A
be
event
that
the
sequence
1010
was
produced
by
the
source.
(a)
[4
points]
Find
P(AISQ).

5,
9
ot
mosd+
2
1%
ooT
o
b
U
D
sel=
()0
)
«
(D)
veude=
i
2
'T
R

LG
I
A
&
Vs
=
p
(Alsy)=
1
"3ng
cedvced

ISL)
59""WL€
§/7
o.ce
5{@
52..
(b)
[6
points]
Find
P(A).
E

',
U?m?

Lo
o
P"GEQ{@,'!%Y
1;})215;]%(\@:!1%&11.?
(7(/3(\:
P\{/ALEE>
(7/§,)
,_,',
{i/(f'fi/!/g{fi
@[5;}
+
V(A/gl)
P(SJ)

~
O

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ol


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