Random variable represents a single-valued result of a random event. Its value is unknown to us, not because of our ignorance, but because of its non-existence. The value exists only after the happening of that random event.
Symbol represents a particular value of . It is an existing value that can be substituted to . We use symbol instead of a number because we have not yet known what that particular number is.
— Me@2016-04-08 05:24:45 PM
X ~ random variable
It is a variable due to the fact that the “identical” random process can result differently at different times.
x ~ a value of X
Since it is a particular value of X, it is not a variable. However, it may seem to be a variable because it may still be unknown to us.
Symbol is meaningless because inside, it must be a statement (representing an event). Symbol is a random variable, not a statement.
Instead, “” is a statement. So expression is meaningful, such as
From another point of view, is a noun phrase, such as “my monthly salary”, not a number. Symbol is a number, although maybe not known yet. That’s why whatever the formula, it contains no ‘s, but ‘s. For example,
— Me@2016-05-04 06:32:24 PM
2023.05.16 Tuesday (c) All rights reserved by ACHK