## Step 1: Analyze the Meaning of a Continuous Random Variable A continuous random variable is a variable that can take any value within a given range, often any value within an interval on the real number line. Unlike discrete random variables, which have outcomes that can be listed or counted, continuous random variables are associated with measurements and can assume an infinite of possible values. ## Step : Examine Each - **A) Finite number of outcomes:** This describes a discrete random variable, not a continuous one. Continuous variables have an infinite number of outcomes within a range. - **B) Countable outcomes:** Countability is a feature of discrete variables, which can be listed or enumerated. - **C) Probability at a point is zero:** For continuous random variables, the probability of the variable taking any exact value is zero. Instead, probabilities are assigned to intervals, not individual points. - **D) Only integer values:** This describes a discrete variable, specifically one that is restricted to integer values. ## Step 3: Identify the Distinguishing Characteristic From the above analysis, the characteristic that uniquely distinguishes a continuous random variable is that the probability at any single point is zero. This is due to the infinite number of possible values in any interval, making the probability of any exact value infinitesimally small. --- ## Final Answer **C) Probability at a point is zero**