Given a gaussian distribution, we draw a $X$ from it. What will the probability of drawing that $X$?
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1$\begingroup$ Welcome to the site. Can you add to your question by describing what you've tried so far and what you need help to understand? Is this a homework/course question? If so, please add the self-study tag. $\endgroup$– IzyCommented Oct 1, 2020 at 15:26
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The probability is zero.
A probability is a length times a width. It is an area. If the height is the density, then the width is zero because it is exactly one point. You can calculate a probability between two points, but not at a point.
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$\begingroup$ I prefer to think of it as 'the probability (of getting any specific number in a Gaussian distribution) is infinitesimally small and therefore approximately equal to zero'. But I like your way of thinking about it too. $\endgroup$– IzyCommented Oct 1, 2020 at 15:30
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$\begingroup$ @Izy I think the proper answer is that it has measure zero because there are a countable number of points (1) mapping onto a continuum. $\endgroup$ Commented Oct 1, 2020 at 15:35
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$\begingroup$ I certainly wouldn't argue with that definition, just thinking back to when I was learning, the way I described it helped me to visualise (& therefore remember) it. $\endgroup$– IzyCommented Oct 1, 2020 at 15:53