Variabel acak kontinyu: Béda antarrépisi

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By one convention, [[variabel acak]] ''X'' is called '''continuous''' if its [[cumulative distribution function]] is [[continuous]]. That is equivalent to saying that Pr[''X'' = ''a''] = 0 for all [[real number]]s ''a'', i.e.: the probability that ''X'' attains the value ''a'' is zero, for any number ''a''.
 
While for a [[discrete random variable]] one could say that an [[event]] with [[probability]] zero is impossible, this can not be said in the case of a continuous random variable, because then no value would be possible.
 
This [[paradox]] is solved by realizing that the probability that ''X'' attains a value in an [[uncountable]] set (for example an [[interval (mathematics)|interval]]) can not be found by adding the probabilities for individual values.
 
By another convention, the term "continuous random variable" is reserved for random variables that have [[probability density function]]s. A random variable with the [[Cantor distribution]] is continuous according to the first convention, and according to the second, is neither continuous nor discrete nor a weighted average of continuous and discrete random variables.
 
In practical applications random variables are often either discrete or continuous.
 
[[en:Continuous probability distribution]]
[[pl:Zmienna losowa ciągła]]