this post was submitted on 21 Sep 2023
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I’m overthinking this.
If everyone gets the full mark, it’s not a random variable anymore, you would have a collapse of the probability distribution, that would tend to a Dirac delta function. In this case, the very definition of “quartiles” would fail. So, yeah, there would be no one there because it wouldn’t exist.
Well it can be a RV. Just one that is uniformly distributed over the set {x}, where x is the full mark score. Or however you want to put it.
It is a rather useless and uninteresting RV but nontheless is is one....