- Thread starter
- #1

- Thread starter JamieLam
- Start date

- Thread starter
- #1

- Feb 13, 2012

- 1,704

Wellcome on MHB JamieLam!...

Basically there are two types of random variables. One type is a r.v. that assume a

Kind regards

$\chi$ $\sigma$

- Admin
- #3

- Mar 5, 2012

- 9,491

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.

- Thread starter
- #4

Thank you Chisigma and I like Serena for the warm welcome and kind guidance, for r.v. that has a discrete set of values, I understand that for real life examples are like dice and coins. Is there any uses for r.v. that uses continuous probability function for real life? I mean I assume there are but I personally do not know any. If you know, please say. Thanks!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.

- Feb 13, 2012

- 1,704

[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 continous 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...

A very important design target in a radio or optical digital receiver is to minimize the

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]

- Thread starter
- #6

Thanks for the information. If you have more examples of the use of continuous probability functions used in stuff that laymen commonly used, please say.

[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 continous 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...

A very important design target in a radio or optical digital receiver is to minimize thebit error rateand 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]

- Mar 3, 2012

- 14

eg the number of seconds elapsed between two busses arriving at the same bus stop could be:

0.0000000000000000000000000000000000000000001

0.000000000000000000000000000002

7.1

or any other arbitrary number