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H(<br />

x)<br />

<br />

[ P(<br />

x<br />

<br />

<br />

P(<br />

x<br />

0)<br />

log P(<br />

x<br />

<br />

<br />

2)<br />

log P(<br />

x<br />

0)<br />

<br />

<br />

2)<br />

P(<br />

x<br />

<br />

<br />

P(<br />

x<br />

1)<br />

log P(<br />

x<br />

<br />

1)<br />

3)<br />

log P(<br />

x<br />

= - [P log Q + Q log Q + Q log Q + P log P]<br />

2P log P 2Q<br />

log Q <br />

H( x)<br />

<br />

2<br />

2<br />

bits/sym. ----(4)<br />

Step – 2: Calculate H(x/y) = P ( xy)<br />

log P ( x / y)<br />

Note, i & j can take values<br />

<br />

i 1 1 2 2<br />

j 1 2 1 2<br />

H(<br />

x / y)<br />

<br />

[ P(<br />

x<br />

P(<br />

x <br />

P(<br />

x <br />

2,<br />

2,<br />

y <br />

i<br />

1,<br />

y 1)<br />

log p(<br />

x 1 / y 1)<br />

P(<br />

x 1,<br />

y 2)<br />

log p(<br />

x 1 / y 2)<br />

Step – 3: Calculate P(x/y) using,<br />

(i) P(x = 1 / y = 1) =<br />

Where,<br />

Input<br />

X<br />

0<br />

1<br />

2<br />

3<br />

2)<br />

log ( x<br />

j<br />

y 1)<br />

log p(<br />

x 2 / y 1)<br />

P(<br />

x<br />

P(y=1) = P(x=1, y=1) + P(x=2, y=1)<br />

2 / y 2)]<br />

P ( x / y)<br />

<br />

1)<br />

. P(<br />

y 1/<br />

x 1)<br />

P(<br />

y 1)<br />

<br />

3)]<br />

P(<br />

x)<br />

. P(<br />

y / x)<br />

P(<br />

y)<br />

= P(x=1) . P(y=1 / x=1) + P(x=2,) . P(y=1 / x=2)<br />

= Q . p + Q . q<br />

= QP + Q (1 – p)<br />

P(<br />

y 1)<br />

Q<br />

1<br />

p<br />

p<br />

1<br />

0<br />

1<br />

1 – p = q<br />

(1 – p) = q<br />

2<br />

3<br />

Output<br />

Y<br />

. ----(5)

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