its continuous because if it was discrete i could measure it right now but its actually over time. For example: if my doctor wants to weigh me ,he will weigh me once and then weigh me again in like 1 week or so
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It is a continuous variable.
It is discrete even though time itself is continuous.
Discrete random variable
Generally continuous but it is discrete if you look at one cupful, two cupfuls, etc (or spoonful or bucketful).
continuos