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**praneethbobba****Member**- Registered: 2013-10-06
- Posts: 5

Hi All

If the mean of a Gaussian random variable is '4' and variance is '3'. Then what is the probability P(X=4) = ?

Anybody aware of this , please help..!!

Thanks in Advance

Praneeth

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Hi

Welcome to the forum!

Are you maybe looking for P(X<=4) or maybe P(X>=4), because, P(X=4) is just 0.

*Last edited by anonimnystefy (2013-10-06 21:24:36)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**praneethbobba****Member**- Registered: 2013-10-06
- Posts: 5

hi anonimnystefy

Nah.. actually i'm looking for the probablity at a specific value of X. Can you explain why it will be Zero ? It would be really helpful

Thanks

Praneeth

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Hi

If X has a continuous distribution, P(X=a) is 0 for any constant a. Since the Gaussian (normal) distribution is continuous, P(X=4).

If you say why you need to calculate that probability, maybe I can help you set it up better.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**praneethbobba****Member**- Registered: 2013-10-06
- Posts: 5

oh.. is it ? Actually that was a question in a text I'm following !! I'm new to this subject ... can you provide any links so that I can get some more understanding on random variable / process concepts ?

Thanks

Praneeth

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Hi

Look at this Wiki article:http://en.m.wikipedia.org/wiki/Continuo … stribution. Under the section Continuous Probability Distribution it is explained why the probability of a single value of a continuous random variable is 0.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**praneethbobba****Member**- Registered: 2013-10-06
- Posts: 5

That's some gud stuff man. Thanks a lot

Praneeth

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

You're welcome!

If you have any other questions be sure to ask!

*Last edited by anonimnystefy (2013-10-06 22:54:43)*

Here lies the reader who will never open this book. He is forever dead.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,538

hi praneethbobba

Welcome to the forum.

In the real world (as distinct from the made up world of mathematics) you can never measure something with complete accuracy.

eg. Let's say a manufacturer makes 10 centimetre rods. Could you ever measure a rod and discover that it is exactly the right length?

How are you measuring it? With a ruler?

The marks on a ruler have thickness so under a microscope where on the ruler are you saying it is 10 cm? (see picture below)

OK. Let's say we decide to use a clever optical measuring device that can achieve an accuracy to the size of a wavelength of light. That still means you have a small amount of doubt about the measurement.

Use an electron microscope? Still limited by the size of an electron.

Measure to the nearest quark? ..... And so on.

In reality, there is no such thing as an exact measurement. The best we can ever do is to say a measure is **x +/- e**, where e is the amount by which our measurement could be wrong.

For that reason the probability of any exact measurement with a continuous distribution will always be zero.

The manufacturer has to proceed like this:

"I know my customers expect the rods to be accurate to 0.01 cm so what's the probability of not getting a reject ie P(9.99 < X < 10.01) ?"

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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