Yes it is.
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If x = 1 then X is not really a random variable but a constant.
A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values.
True
How often the value of a random variable is at or below a certain value.
A random variable is a variable which can take different values and the values that it takes depends on some probability distribution rather than a deterministic rule. A random process is a process which can be in a number of different states and the transition from one state to another is random.