The discussion revolves around the practical uses and theoretical understanding of continuous probability distributions. Participants explore whether these distributions are merely mathematical constructs or if they have real-world applications, particularly in fields like digital transmission and everyday scenarios.
Participants generally agree that continuous probability distributions have practical applications, but the specific examples and contexts remain varied and somewhat unresolved. Multiple viewpoints on the extent and nature of these applications are present.
Some limitations include the lack of consensus on specific examples of continuous probability functions in everyday life and the dependence on definitions of random variables. The discussion does not resolve the complexities involved in applying these concepts practically.
This discussion may be useful for individuals interested in the applications of probability theory in real-world scenarios, particularly in fields like digital communications, statistics, and general science.
JamieLam said:Hi, I'm not sure if this has been brought up before. I'm a non-mathematician. I like to know what's the use of continuous probability distribution. Is there any use for it, is it merely a mathematical object or has it real(practical uses for it) If there are practical uses for it, what is it been use for? Thank you very much
JamieLam said:Hi, I'm not sure if this has been brought up before. I'm a non-mathematician. I like to know what's the use of continuous probability distribution. Is there any use for it, is it merely a mathematical object or has it real(practical uses for it) If there are practical uses for it, what is it been use for? Thank you very much
I like Serena said:One of the continuous distributions is the so called normal distribution, which is shaped like a bell curve.
The normal distribution is extensively applied in many, many sciences, including physics, psychology, and business.
chisigma said:A suggestive example comes from my experience in the field of digital transmission, i.e. the medium that supports for You Internet, Smartphone, GPS and other modern services. The transmitted signal s(t) is a sequence of symbols, one any T seconds and the sequence is recovered sampling in appropiate way the received signal any T seconds. The received signal r(t) is the sum of an highly attenuated reply of the transmitted signal and thermal noise of the electonic circuits of the reciever so that can be written as...
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Now n(t) is a continuos r.v. that is described in term of continuous probability function. If for example thye tramsitted signal is a sequence of binary symbols, each with possible values + 1 or - 1, if in the sampling time t the istantaneous value of the noise n(t) overcomes s(t), then You have an erroneous recovered symbol, i.e. a trasmitted 1 is sampled as -1 or vice versa. In the figure You can see a binary received signal corrupted by noise...
http://ddpozwy746ijz.cloudfront.net/c1/78/i83392705._szw380h285_.jpg
A very important design target in a radio or optical digital receiver is to minimize the bit error rate and an essential role to meet that is the statistical analysis of noise resistance of the receiver...
Kind regards
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