# extra 2 - convenient to use and some PDF is more...

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1 PDF and CDF We have studied two types of probability functions: CDF P ( x ) and PDF p ( x ). Why do we need to use both of them? Answer: The advantage of CDF is easy to understand. We can easily understand the meaning of a CDF such as P ( x ) = Pr{ X x }. The definition of PDF p ( x ) involves integration, which is somehow not so direct. However, it is less informative when we use a CDF. For example, if I ask you which values of x have high probabilities given the CDF below. This is relatively not so direct to see. (The answer is the range where the derivative is large.) For a PDF, it is quite straightforward to see the range with the large probabilities. Such a range is where the PDF value is large (such as 1.65m for man below). In fact, CDF and PDF mean the same thing using two different ways. Sometimes CDF is sometimes more

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Unformatted text preview: convenient to use and some PDF is more convenient. Therefore we usually introduce both of them. x P ( x ) height 1.65m mean for men p ( x ) 2 PDF A PDF is usually obtained through experiments. For example, to character peoples, heights, we need many data from hospital or other sources. These PDFs can be very useful. For example, the they can be used to design, e.g., cloth, chairs, cars, doors, etc. Note that something may happen beyond our expectation. Think about Yao Ming comes to a bicycle shop to buy a bicycle! 100% error-free is not the principle of communication systems. We need a realistic performance criterion. Why? height 1.55m mean for women 1.65m mean for men p ( x )...
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## This note was uploaded on 01/11/2011 for the course EE 3008 taught by Professor Pingli during the Fall '08 term at City University of Hong Kong.

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extra 2 - convenient to use and some PDF is more...

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