The Importance of Statistic and Probability in Electrical and Computer Engineering ~ Official Notes

A Research on the Role of
Statistic and Probability in ELECTRICAL and COMPUTER ENGINEERING

                        Electrical and Computer engineers have played a central role in the design of modern information and communications systems. Practical current applications from various areas of electrical and computer engineering are used to show how averages and relative frequencies provide the proper tools for handling the design of systems that involve randomness. These application areas include wireless and digital communications, digital media and signal processing, system reliability, computer networks, and Web systems. This research aims to point out the important role of Statistic and Probability in the field of Electrical Engineering.

General Role of Statistic and Probability

1.      Mathematical models relate important system parameters and variables using mathematical relations. They allow system designers to predict system performance by using equations when experimentation is not feasible or too costly.

2.      Computer simulation models are an alternative means of predicting system performance. They can be used to validate mathematical models.

3.      In deterministic models the conditions under which an experiment is performed determine the exact outcome. The equations in deterministic models predict an exact outcome.

4.      In probability models the conditions under which a random experiment is performed determine the probabilities of the possible outcomes. The solution of the equations in probability models yields the probabilities of outcomes and events as well as various types of averages.

5.      The probabilities and averages for a random experiment can be found experimentally by computing relative frequencies and sample averages in a large number of repetitions of a random experiment.

6.      The performance measures in many systems of practical interest involve relative frequencies and long-term averages. Probability models are used in the design of these systems.

Some of the Specific Application of Statistic and Probability

1.      Computer memories
    Suppose you are designing a computer memory to hold k-bit words. To increase system reliability, you employ an error-correcting-code system. With this system, instead of storing just the k data bits, you store an additional l bits (which are functions of the data bits). When reading back the (k+l)-bit word, if at least m bits are read out correctly, then all k data bits can be recovered (the value of m depends on the code). To characterize the quality of the computer memory, we compute the probability that at least m bits are correctly read back. You will be able to do this after you study the binomial random variable.

2.      Optical communication systems
     Optical communication systems use photodetectors to interface between optical and electronic subsystems. When these systems are at the limits of their operating capabilities, the number of photoelectrons produced by the photodetector is well-modeled by the Poisson random. In deciding whether a transmitted bit is a zero or a one, the receiver counts the number of photoelectrons and compares it to a threshold. System performance is determined by computing the probability that the threshold is exceeded.

3.      Wireless communication systems
    In order to enhance weak signals and maximize the range of communication systems, it is necessary to use amplifiers. Unfortunately, amplifiers always generate thermal noise, which is added to the desired signal. As a consequence of the underlying physics, the noise is Gaussian. Hence, the Gaussian density function which plays a prominent role in the analysis and design of communication systems.

4.      Variability in electronic circuits.
   Although circuit manufacturing processes attempt to ensure that all items have nominal parameter values, there is always some variation among items. How can we estimate the average values in a batch of items without testing all of them? How good is our estimate? You will learn how to do this when you study parameter estimation and confidence intervals. Incidentally, the same concepts apply to the prediction of presidential elections by surveying only a few voters.

5.      Computer network traffic.
    Prior to the 1990s, network analysis and design was carried out using long-established Markovian models. You will study Markov chains. As self-similarity was observed in the traffic of local-area networks, wide-area networks, and in World Wide Web traffic, a great research effort began to examine the impact of self-similarity on network analysis and design. This research has yielded some surprising insights into questions about buffer size vs. bandwidth, multiple time- scale congestion control, connection duration prediction, and other issues.