Question

A random variable is said to be continuous if it

Check all that apply.
1) has a countably infinite number of values.
2) is measured over an interval.
3) can have decimal values.
4) has a countable number of values

Answer 1

A random variable is said to be continuous if it is measured over an interval and can have decimal values. Correct option is 2.

Step-by-step explanation:

A random variable is said to be continuous if it is measured over an interval and can have decimal values.

1. Has a countably infinite number of values: This applies to a discrete random variable, not a continuous random variable.
2. Is measured over an interval: This is a characteristic of a continuous random variable. For example, the temperature of a randomly selected day in a city, or the height of a randomly selected high school student.
3. Can have decimal values: This is also a characteristic of a continuous random variable. Examples include temperature measurements, or the weight of an object.
4. Has a countable number of values: This is incorrect. A continuous random variable does not have a countable number of values, as it can have an infinite number of values within a given interval.