Given the following table showing the possible values of a random variable $X$ and their probabilities: Value of $X$: $0$, $1$, $2$, $3$; Probability: $0.1$, $0.3$, $0.4$, $0.2$. Is the random variable $X$ discrete or continuous? Explain your answer.

• A. $X$ is a discrete random variable because it can take on any value between $0$ and $3$.
• B. $X$ is a discrete random variable because it takes on a finite set of distinct values, each with a specific probability.
• C. $X$ is a continuous random variable because its probabilities are given in a table.
• D. $X$ is a continuous random variable because it can take on any value within an interval.

Answer: (B)

Verified step by step guidance

1. Identify the type of random variable by examining the values it can take. Here, X takes on specific values: 0, 1, 2, and 3.
2. Recall that a discrete random variable takes on countable, distinct values, often integers or specific points, each with an assigned probability.
3. Recognize that a continuous random variable can take on any value within an interval, and probabilities are described by a probability density function rather than specific probabilities for exact values.
4. Since the problem provides a list of distinct values with associated probabilities, this matches the definition of a discrete random variable.
5. Conclude that X is discrete because it takes on a finite set of distinct values, each with a specific probability.