Yes, some of the do exist.
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A categorical variable (also known as a discrete variable) is one whose range is countable; e.g. the variable answ has values [yes, no, not sure]. answ is a categorical variable with range 3.A continuous variable is one which is not categorical; e.g. weight is a continuous variable which can take any value between 0 and 1000 kg (say) for a human being.
It is a continuous variable.
Yes. It is a continuous variable. As used in probability theory, it is an example of a continuous random variable.
No, Patient's gender is not a continuous variable. It is discrete variable.
No, it is a continuous process but not a continuous variable. The magnitude of star-shine, across all stars is a continuous variable. The magnitude of a star's shine over time is a continuous variable.