In probability, sample space is a set of all possible outcomes of an experiment.
A sample space can be finite or infinite.
A sample space can be discrete or continuous.
A sample space can be countable or uncountable.
From some texts I got that finite sample space is same as discrete sample space and infinite sample space is continuous sample space.
But some texts are saying that countable sample space is discrete sample space and uncountable sample space is continuous sample space.
Which one of the following above is correct?
I got confuse because of the following two statements in this text book
Discrete Probability Law :
If the sample space consists of a finite number of possible outcomes, then the probability law is specified by the probabilities of the events that consist of a single element. In particular, the probability of any event $\{s_1, s_2, . . . , s_n\}$ is the sum of the probabilities of its elements.
Continuous Models :
Probabilistic models with continuous sample spaces differ from their discrete counterparts in that the probabilities of the single-element events may not be sufficient to characterize the probability law.
Discrete probability law deals with finite sample spaces, but continuous probability models deal with continuous sample spaces. So I am confused whether countably finite sample spaces comes under which probabilistic model.
listen this also for accuracy.