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"Suppose a species of bacteria typically lives 4 to 6 hours. What is the probability that a bacterium lives exactly 5 hours? The answer is actually 0%. A lot of bacteria live forapproximately 5 hours, but there is no chance that any given bacterium dies at exactly 5.0000000000... hours."

I was reading the Wikipedia page on probability density function and this was the analogy used to explain the concept of distribution function. Now, the idea of pdf as the rate of change of probability with change in variable's value is clear to me.

However, i am not being able to justify the statement that probability at a point given with infinite precision is undefined and we can talk of it only in an interval(starting with the infinitesimal dx).

Sparsh Sharma
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    Why do you consider this a physics question about QM? – innisfree Jun 11 '16 at 09:41
  • well, you are right. Actually, i came into this when i started quantum mechanics, so i tagged it mistakenly –  Jun 11 '16 at 09:45
  • This is a question about mathematics, not physics. Not even the context is physics. Have you tried posting in Mathematics SE? – sammy gerbil Jun 11 '16 at 11:53
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    No, this is not a question about mathematics either. It is in fact not a question, period. – WillO Jun 11 '16 at 12:41
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    "the statement that probability at a point given with infinite precision is undefined" Who says so? Actually, the probability that a continuous random variable equals a given point is quite well defined (and is zero). – Did Jun 11 '16 at 16:19
  • Your question has been asked often on this site. Search for "probability point zero" and you'll find several versions. This one may help: http://math.stackexchange.com/questions/1548914/non-integral-over-a-point-proof-that-the-probability-of-any-point-in-a-continuou – Ethan Bolker Jun 11 '16 at 16:21

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The probability is the fraction of total area under the Normal Distribution Curve between two limits. If the two limits coincide, there is zero area between them.

sammy gerbil
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