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3.1 Equivalent Continuous pdf's

It will be convenient to express a discrete pdf as a continuous pdf using ``delta functions''. This will make the ensuing discussion easier to follow and simplifies many of the manipulations for discrete pdf's. Given a discrete pdf , let us associate event i with the discrete r.v. , and then define an equivalent ``continuous'' pdf as follows:

Here is the ``delta'' function and it satisfies the following properties: