Final answer:
The random variable X is discrete since it represents countable outcomes (1 for colonial and 0 for non-colonial houses), thus the statement that X is continuous is false.
Step-by-step explanation:
The random variable X described in the question takes on the value 1 if a house is colonial and the value 0 if the house is not colonial. This means that X can only take on a finite number of distinct values, which are countable. Therefore, we can categorically state that the random variable X is not a continuous random variable, but a discrete random variable. A continuous random variable, by definition, would take an infinite number of possible values within a given range, which are the results of measurements, not countable entities. In the case of X = 1 or 0 depending on the house style, this indicates the outcomes are countable, and so this random variable is discrete. Hence, the statement 'The random variable X is continuous' is false.