Question

Given a circle of radius $R$, the experiment is to randomly select a chord in that circle. Identify the type of the sample space.

• A. Finite sample space
• B. Continuous sample space
• C. Infinite discrete sample space
• D. None of these

Answer 1

The correct option is B Continuous sample space

Given a circle of radius $R$, the experiment is to randomly select a chord in that circle.

There are many ways to accomplish such a selection.

However the sample space is always the same:

$\{AB:AandBarepointsonagivencircle\}$.

One natural random variable defined on this space is the length of the chord.

Here the length of the chord takes more values depending on the point we choose in the circle.

We know that, "A continuous sample space is one which takes values in one or more intervals."

Therefore, this is a continuous sample space.