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What is the difference between Discrete and Continuous Random Variables?

Discrete Random Variable = takes countable or discretely determinable values. So, it is always listable. For example, digital signals.

Continuous Random Variable = takes continuous values. So, it always has a range. For example, analog signals.

Am I correct?

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It merely depends on how the values are measured. Think of a water faucet that is filling a mug drop by drop, that is a discrete filling. If the water facet fills it with a water jet, it is filled continuously.

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