The Gaussian density function is the most important of all the densities and it enters into the areas of science and engineering.This importance stems from its accurate description of many practical and significant real-world quantities, especially when such quantities are the result of many small independent random effects acting to create the quantity of interest.
The Binomial density can be applied to the Bernoulli trial experiment.It applies to many games of chance,detection problems in radar and sonar, and many experiments having only two possible outcomes on any given trial.
The Rayleigh density function describes the envelope of one type of noise when passed through a band pass filter.It is also important in analysis of errors in various measurement systems.
The Exponential density is useful in describing raindrop sizes when a large number of rainstorm measurements are made.It is also known to approximately describe the fluctuations in signal strength recieved by radar from certain types of aircraft.
The Uniform density finds a number of practical uses.A particularly important application is in the quantization of signal samples prior to encoding in digital communication systems.Quantization amounts to "rounding off" the actual sample to the nearest of a large number of discrete "quantum levels". The errors introduced in the round-off process are uniformly distributed.
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