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...
[FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]r[/FONT][/FONT][FONT=MathJax_Main][FONT=7253d757afc94e7c081a2160#081300]([/FONT][/FONT][FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]t[/FONT][/FONT][FONT=7253d757afc94e7c081a2160#081300][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][/FONT][FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]a[/FONT][/FONT][FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]s[/FONT][/FONT][FONT=MathJax_Main][FONT=7253d757afc94e7c081a2160#081300]([/FONT][/FONT][FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]t[/FONT][/FONT][FONT=7253d757afc94e7c081a2160#081300][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][/FONT][FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]n[/FONT][/FONT][FONT=MathJax_Main][FONT=7253d757afc94e7c081a2160#081300]([/FONT][/FONT][FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]t[/FONT][/FONT][FONT=7253d757afc94e7c081a2160#081300][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])[/FONT][/FONT][FONT=7253d757afc94e7c081a2160#081300][/FONT]
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
[FONT=ea9bd3dac1f0b279081a2160#081300][FONT=MathJax_Math-italic]χ[/FONT][/FONT] [FONT=MathJax_Math-italic][FONT=ea9bd3dac1f0b279081a2160#081300]σ[/FONT][/FONT][FONT=ea9bd3dac1f0b279081a2160#081300][/FONT]
A continuous probability distribution is a mathematical function that describes the probability distribution of a continuous random variable. It assigns probabilities to intervals of values instead of individual values, and the probabilities are represented by the area under the curve of the function.
A continuous probability distribution is used for continuous random variables, such as measurements that can take on any value within a certain range. A discrete probability distribution is used for discrete random variables, such as counts or whole numbers. In a continuous distribution, the probabilities are represented by the area under the curve, while in a discrete distribution, the probabilities are represented by individual values.
Some common examples of continuous probability distributions include the normal distribution, the exponential distribution, and the uniform distribution. These distributions are often used to model real-world phenomena, such as heights and weights of individuals, waiting times, and random variables with equal probabilities.
The probability density function (PDF) is a mathematical function that describes the relative likelihood of a continuous random variable taking on a particular value. It is used to represent the probability distribution of a continuous random variable and is directly related to the area under the curve of the continuous distribution function.
Continuous probability distributions are useful in research and analysis because they allow for the calculation of probabilities for a wide range of values. They can be used to model real-world data, make predictions, and estimate the likelihood of certain events or outcomes. They are also used in statistical tests and hypothesis testing to determine the significance of results.