If the sample space $\delta$ is an infinite set, does this necessarily imply that any random variable X defined from S will have an infinite set of possible values? If yes, say why. If no, give an example.

Question

Quizplus · Accepted Answer

The Answer is No. In the experiment in which a coin is tossed repeatedly until an H results, let Y = 1 if the experiment terminates with at most 5 tosses and Y = 0 otherwise. The sample space is infinite, yet Y has only two possible values.

If the Sample Space δ\deltaδ Is an Infinite Set, Does This Necessarily Imply That Any

If the Sample Space $\delta$ Is an Infinite Set, Does This Necessarily Imply That Any