Question

determine whether the random variable x is discrete or continuous. explain. let x represent the number of fish caught during a fishing tournament. choose the correct answer below. a. the random variable is discrete, because it has an uncountable number of possible outcomes. b. the random variable is continuous, because it has an uncountable number of possible outcomes. c. the random variable is discrete, because it has a countable number of possible outcomes. d. the random variable is continuous, because it has a countable number of possible outcomes.

Explanation:

Step1: Recall Discrete/Continuous Definitions

Discrete random variables have countable (finite or infinite but listable) outcomes (e.g., number of items). Continuous have uncountable (infinite, non - listable) outcomes (e.g., time, weight).

Step2: Analyze the Random Variable \( x \)

\( x \) is the number of fish caught. The number of fish can be \( 0, 1, 2, \dots \), which is a countable set (we can list the possible values: 0, 1, 2, 3, …). So \( x \) is discrete because it has a countable number of possible outcomes.

Step3: Evaluate the Options

• Option A: Says discrete with uncountable outcomes. Incorrect, discrete has countable.
• Option B: Says continuous with uncountable. But \( x \) is discrete, so incorrect.
• Option C: Says discrete with countable outcomes. Correct.
• Option D: Says continuous with countable. Incorrect, continuous has uncountable and \( x \) is discrete.

Answer:

C. The random variable is discrete, because it has a countable number of possible outcomes.