Continuous random variables are outcomes that take on any numerical value in an interval as a result of conducting an experiment?
Close, but not quite
Close, but not quite. Continuous random variables are outcomes that can take on any value within a given range or interval, rather than any numerical value. This means that the possible outcomes of an experiment involving a continuous random variable can be infinitely many within a specific interval.
To give you a better understanding, let’s consider an example. Suppose we want to measure the height of students in a school. Since height can vary continuously, we can think of it as a continuous random variable.
If we conduct an experiment to measure the heights of students, the possible outcomes can be any value within a range, such as from 150 cm to 190 cm. This means that a student can have a height of 152 cm, 167.5 cm, or any other value within that interval. It is important to note that the height of a student can take on any decimal value within that interval, not just whole numbers.
In contrast, discrete random variables can only take on specific numerical values, usually whole numbers. For example, if we were counting the number of students in a classroom, we could only have whole numbers, such as 20 students, 21 students, or 22 students. There wouldn’t be any 21.5 students since we can’t have a fraction of a student.
So, to summarize, continuous random variables can take on any value within a specific interval, while discrete random variables can only take on specific numerical values.
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