I've read :The probability that a continuous random variable will assume a particular value is zero.
Why is that? Could someome explain to me with a clear example?
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1See this video by PBS Infinite Series. They address precisely this question around the six minute mark (using a dart-board as an example of a continuous distribution). – Bobson Dugnutt Aug 17 '17 at 16:00
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It is not the formal definition, but I think it like this. Assume you have a square area, and the size of one of the edge is 5. That is, the area is 25. And there are uniformly distributed 5 balls in that area. What is the probability that you grab a ball from that square area when your eyes are covered ?
5 / 25 right ? This is the relation of density and probability.
Lets turn back to continuous distribution. For example Gauss. You want to know the probability of 3 from a gauss distribution $g(\mu,\sigma)$. It is 0. because probability is 1\infinity. Why infinity ? Because under the Gaussian curve there are infinite number of possible real number !
So lets pick an interval. 3 - 3.1 then the probability is selected area / whole area (As in the first example)
This is not the formal definition. As you can find the formal one every where ... If I am mistaken please some one fix me as well :)
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