'Note that a sample of random variables (i.e. a set of measurable functions) must not be confused with the realizations of these variables (which are the values that these random variables take). In other words, X i is a function representing the measurement at the i-th experiment and x i = X i ( ω ) is the value we actually get when making the measurement.''I'm afraid I don't understand this passage, can anybody please explain the point?

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&#039;Note that a sample of random variables (i.e. a set of measurable functions) must not be confused with the realizations of these variables (which are the values that these random variables take). In other words,       X    i   is a function representing the measurement at the   i-th experiment and       x    i    =      X    i    (      ω    ) is the value we actually get when making the measurement.&#039;&#039;I&#039;m afraid I don&#039;t understand this passage, can anybody please explain the point?

iberistazi · Accepted Answer

At best, WP&#039;s wording is unclear. In particular, the second statement from the OP seems to allude to a separation between intervals and exact values, measurement precision, approximations, or any combination of these. Such information is irrelevant. Instead, one wants to set a function apart from one of its values. For functions from&amp;nbsp;E&amp;nbsp;to&amp;nbsp;F, say, the first one is an element of&amp;nbsp;F&amp;nbsp;E&amp;nbsp;and the second one is an element of&amp;nbsp;F&amp;nbsp;(and in probability theory,&amp;nbsp;E&amp;nbsp;is often denoted by&amp;nbsp;Ω&amp;nbsp;and&amp;nbsp;F&amp;nbsp;could be&amp;nbsp;R&amp;nbsp;or a power of&amp;nbsp;R&amp;nbsp;, but this is not important).

Note that a sample of random variables (i.e. a set of measurable functions) must not be confused wit

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