(label:clarified, math_stat)

See the other post on 0 probability vs 0 density.

Eg: Suppose I ask you to cut a 5-meter-long string by throwing a knife. What's the distribution of the longer piece's length? There is a pdf f(x). Bell-shaped, since the most people will aim at the center.

This f(x) = 0 for x > 5 i.e. zero density.

For the same reason, Pr(X > 5) = 0 i.e. no uncertainty, 100% guaranteed.

Here's my idea of probability density at x=4.98. If a computer simulates 100 billion trials, will there be some hits within the neighbourhood around x=4.98 ? Very small but positive density. In contrast, the chance of hitting x=5.1 is zero no matter how many times we try.

By the way, due to the definition of density function, f(4.98) > 0 but Pr(X=4.98) = 0, because the range around 4.98 has zero width.

## Friday, December 11, 2015

### 0 probability ^ 0 density, briefly

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