Sorry if this question is so basic, it hurts. I feel like not understanding this topic well enough is holding me back. If any of this language is wrong in some fundamental way, please correct me! Moving on..
Say I make a probabilistic statement about a random variable $X$ drawn from some unknown continuous distribution:
$$Pr(X > t) < t$$
Assume that statement holds for all $t > 0$.
Now let's say I draw a sample $Y$ from the distribution of $X$, but I don't tell you what $Y$ is. Is there any real difference between reasoning about $Y$ and reasoning about $X$? Is $Y$ a random variable? Does $X = Y$? Does the following implicitly hold?
$$Pr(Y > t) < t$$
Now let's say we do know the value of $Y$, e.g. $Y = 2$. Would probabilistic statements about random variable $Y$ still apply? Or would they go out the window with knowing the variable? Specifically, would the following hold?
$$Pr(2 > t) < t$$