A random variable is ____ if it can assume any numerical value within an interval as a result of measuring the outcome of an experiment.

A random variable is ____ if it can assume any numerical value within an interval as a result of measuring the outcome of an experiment.

• A. Discrete random variable
• B. Bernoulli variable
• C. Continuous random variable
• D. Poisson variable

Answer: (C)

Continuous random variables can take any value within an interval because measurements can be made with arbitrary precision, yielding real numbers like 6.123, 6.4567, or any value in the range. This means the outcome isn’t restricted to separate steps or counts but can fill an entire continuum. In contrast, discrete random variables only take specific values, such as whole numbers; a Bernoulli variable has just two outcomes; a Poisson variable counts events and thus produces nonnegative integers. So the statement describes a continuous random variable.

Continuous random variables can take any value within an interval because measurements can be made with arbitrary precision, yielding real numbers like 6.123, 6.4567, or any value in the range. This means the outcome isn’t restricted to separate steps or counts but can fill an entire continuum. In contrast, discrete random variables only take specific values, such as whole numbers; a Bernoulli variable has just two outcomes; a Poisson variable counts events and thus produces nonnegative integers. So the statement describes a continuous random variable.