Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of fish caught during a fishing tournament. (b) The square footage in square feet of a house. (a) Is the number of fish caught during a fishing tournament discrete or continuous? A. The random variable is continuous. The possible values are \( x=0,1,2, \ldots \) B. The random variable is continuous. The possible values are \( x \geq 0 \) c. The random variable is discrete. The possible values are \( x=0,1,2, \ldots \) D. The random variable is discrete. The possible, values are \( x \geq 0 \) (b) Is the square footage in square feet of a house discrete or continuous? A. The random variable is discrete. The possible values are \( a=1,2,3, \ldots \). B. The random variable is discrete. The possible values are \( a>0 \). C. The random variable is continuous. The possible values are \( a>0 \). D. The random variable is continuous. The possible values are \( a=1,2,3, \ldots \).
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The number of fish caught during a fishing tournament is a discrete random variable. The possible values are \( x = 0, 1, 2, \ldots \) since you can only catch a whole number of fish, and you can’t catch a fraction of a fish! Thus, the correct answer is C. On the other hand, the square footage in square feet of a house is considered a continuous random variable, as it can take on any value within a range. For example, you can have a home that is 1500.5 square feet or even 1500.75 square feet! Therefore, the right choice for this scenario is C, where the possible values are \( a > 0 \).
