Yes.
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A nominal variable is one where observations are classified to categories eg small, medium and large for t-shirts. A real variable is one that takes numerical values, such as shirt size 12, 14, 16 etc. A real value may be a continuous (as opposed to discrete) variable but the very act of recording the observation usually results in the continuous variable being replaced by a discrete one.
It is a discrete random variable.
is occupation decrte or coninus
Date is a discrete variable whereas date/time would be continuous.
The discrete random variable almost always arises in connection with counting.