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Post Reopened by Jukka Kohonen, bof, Daniele Tampieri, Dag Oskar Madsen, Yemon Choi
clarify wording, grammar
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Jukka Kohonen
Jukka Kohonen
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Let's consider a continuous random variable $X$ distributed according to a PDF $p(x):\mathbb{R}\mapsto \mathbb{R}_{\geq 0}$.

Is there a meaningful sense in which one could say that for any $x_0:p(x_0)=0$ the event $X=x_0$ is impossible? By impossible, I mean that if we simulate $X$ then we never observe in the sample the value $x_0$.

If the answer is no, how do we make sure that $X$ will never get the value $x_0$?

Note that my question is complementary tonot about the well-known fact that any event of the form $X=x_0$ is almost impossible, in the sense that $\mathbb{P}(X=x_0)=0$, and this does not meansmean that such events cannot happen (i.e., if we simulate $X$ then we can observe the value $x_0$ in the sample).

Let's consider a continuous random variable $X$ distributed according to a PDF $p(x):\mathbb{R}\mapsto \mathbb{R}_{\geq 0}$.

Is there a meaningful sense in which one could say that for any $x_0:p(x_0)=0$ the event $X=x_0$ is impossible? By impossible, I mean that if we simulate $X$ then we never observe in the sample the value $x_0$.

If the answer is no, how do we make sure that $X$ will never get the value $x_0$?

Note that my question is complementary to the well-known fact that any event of the form $X=x_0$ is almost impossible, in the sense that $\mathbb{P}(X=x_0)=0$, and this not means that such events cannot happen (i.e., if we simulate $X$ then we can observe the value $x_0$ in the sample).

Let's consider a continuous random variable $X$ distributed according to a PDF $p(x):\mathbb{R}\mapsto \mathbb{R}_{\geq 0}$.

Is there a meaningful sense in which one could say that for any $x_0:p(x_0)=0$ the event $X=x_0$ is impossible? By impossible, I mean that if we simulate $X$ then we never observe in the sample the value $x_0$.

If the answer is no, how do we make sure that $X$ will never get the value $x_0$?

Note that my question is not about the well-known fact that any event of the form $X=x_0$ is almost impossible, in the sense that $\mathbb{P}(X=x_0)=0$, and this does not mean that such events cannot happen (i.e., if we simulate $X$ then we can observe the value $x_0$ in the sample).

Slight change in wording to emphasize the crux of the question (simulations)
Added to review
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Jukka Kohonen
Jukka Kohonen
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Let's consider a continuous random variable $X$ distributed according to a PDF $p(x):\mathbb{R}\mapsto \mathbb{R}_{\geq 0}$. 

Is it correct tothere a meaningful sense in which one could say that for any $x_0:p(x_0)=0$ the event $X=x_0$ is impossible? By impossible, I mean that if we simulate $X$ then we never observe in the sample the value $x_0$.

If the answer is no, how do we make sure that $X$ will never get the value $x_0$?

Note that my question is complementary to the well-known fact that any event of the form $X=x_0$ is almost impossible, in the sense that $\mathbb{P}(X=x_0)=0$, and this not means that such events cannot happen (i.e., if we simulate $X$ then we can observe the value $x_0$ in the sample).

Let's consider a random variable $X$ distributed according to a PDF $p(x):\mathbb{R}\mapsto \mathbb{R}_{\geq 0}$. Is it correct to say that for any $x_0:p(x_0)=0$ the event $X=x_0$ is impossible? By impossible, I mean that if we simulate $X$ then we never observe in the sample the value $x_0$.

If the answer is no, how do we make sure that $X$ will never get the value $x_0$?

Note that my question is complementary to the well-known fact that any event of the form $X=x_0$ is almost impossible, in the sense that $\mathbb{P}(X=x_0)=0$, and this not means that such events cannot happen (i.e., if we simulate $X$ then we can observe the value $x_0$ in the sample).

Let's consider a continuous random variable $X$ distributed according to a PDF $p(x):\mathbb{R}\mapsto \mathbb{R}_{\geq 0}$. 

Is there a meaningful sense in which one could say that for any $x_0:p(x_0)=0$ the event $X=x_0$ is impossible? By impossible, I mean that if we simulate $X$ then we never observe in the sample the value $x_0$.

If the answer is no, how do we make sure that $X$ will never get the value $x_0$?

Note that my question is complementary to the well-known fact that any event of the form $X=x_0$ is almost impossible, in the sense that $\mathbb{P}(X=x_0)=0$, and this not means that such events cannot happen (i.e., if we simulate $X$ then we can observe the value $x_0$ in the sample).

Post Closed as "Not suitable for this site" by R W, Steven Landsburg, Ryan Budney, Daniele Tampieri, Max Horn
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matteogost
matteogost
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On Impossible events

Let's consider a random variable $X$ distributed according to a PDF $p(x):\mathbb{R}\mapsto \mathbb{R}_{\geq 0}$. Is it correct to say that for any $x_0:p(x_0)=0$ the event $X=x_0$ is impossible? By impossible, I mean that if we simulate $X$ then we never observe in the sample the value $x_0$.

If the answer is no, how do we make sure that $X$ will never get the value $x_0$?

Note that my question is complementary to the well-known fact that any event of the form $X=x_0$ is almost impossible, in the sense that $\mathbb{P}(X=x_0)=0$, and this not means that such events cannot happen (i.e., if we simulate $X$ then we can observe the value $x_0$ in the sample).