Given the following table showing the possible values of a random variable $X$ and their probabilities: Value of $X$: 0, 1, 2; Probability: 0.2, 0.5, 0.3. Is the random variable $X$ discrete or continuous? Explain your answer.

• A. The random variable $X$ is discrete because it takes on a finite set of distinct values, each with a specific probability.
• B. The random variable $X$ is discrete because it can take on any value between 0 and 2.
• C. The random variable $X$ is continuous because it can take on any value within an interval.
• D. The random variable $X$ is continuous because its probabilities add up to 1.

Answer: (A)

Verified step by step guidance

1. Identify the type of values the random variable X can take. Here, X takes on the values 0, 1, and 2, which are distinct and countable.
2. Recall the definition of a discrete random variable: it takes on a countable number of distinct values, each with an associated probability.
3. Recall the definition of a continuous random variable: it can take on any value within an interval or range, often involving infinitely many possible values.
4. Check the probabilities given for each value of X: 0.2, 0.5, and 0.3. These probabilities correspond to specific, separate values rather than a range of values.
5. Conclude that since X takes on a finite set of distinct values with specific probabilities, X is a discrete random variable.