Is the response to the survey question "did you smoke in the last week question mark "response to the survey question "did you smoke in the last week? ":
a discrete random variable,
a continuous random variable,
not a random variable?

The response to the question is a discrete random variable.

Explanation:

By definition of a discrete random variable we infer that the response can only take certain known values  but the response shall be completely random. As an example when we toss a fair coin the out comes are discrete as only either head or tail is possible and the outcome is random meaning we cannot predict the outcome before hand.

Similarly an continuous random variable takes any value in a set and there are infinitely many possible values it can take. For example if we choose any real number between 1 and 10. Since the answers are infinitely many in number and are completely random.

Now in our survey we can infer that the responses shall be either "yes I smoked last week" or "No i didn't smoke last week". Hence the variables are discrete and random.

not a random variable

Explanation:

Because the value is not numerical.

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