In,

*Y*may be the same as the input symbols

*X*, i.e.,

*X*=

*Y*.

However in most cases and hence in general,

*X*≠

*Y*.

**directed graphs**.

*Example use of Directed Graphs:*

If,

*p*(

*x*) are

_{i}*p*(

*x*

_{0}) = 0.4

*p*(

*x*

_{1}) = 0.6

*p*(

*y*|

_{j}*x*) are

_{i}*p*(

*y*

_{0}|

*x*

_{0}) = 0.80

*p*(

*y*

_{0}|

*x*

_{1}) = 0.00

*p*(

*y*

_{1}|

*x*

_{0}) = 0.15

*p*(

*y*

_{1}|

*x*

_{1}) = 0.05

*p*(

*y*

_{2}|

*x*

_{0}) = 0.05

*p*(

*y*

_{2}|

*x*

_{1}) = 0.15

*p*(

*y*

_{3}|

*x*

_{0}) = 0.00

*p*(

*y*

_{3}|

*x*

_{1}) = 0.80

*x*

_{0},

*x*

_{1},

*y*

_{0},

*y*

_{1},

*y*

_{2}and

*y*

_{3}by ⬤ such that,

The known **transitional probabilities** can help us draw **directed arrows** between ⬤ of *X* and ⬤ of *Y*.

Therefore,

*p*(

*x*) and

_{i}*p*(

*y*|

_{j}*x*) are known,

_{i}*p*(

*y*) is given by,

_{j}*p*(

*y*) = transitional probability ×

_{j}*p*(

*x*)

_{i}