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"Sample space" hints very very heavily that we're going to be talking about probabilities, i.e. that there will be one (or more) probability measure functions defined on our sample space. (Technically they are defined on " $\sigma$ -algebras", which are sets of events in our sample space satisfying certain properties, but the distinction is ...
If you call the event space to be the space of all events, then in this case the event space here will be the power set of $\{1,2,3,4,5,6\}$ just as you mentioned. The relevant model assigns a probability equal to $\frac{\#\text{event}}{6}$ to an event. The event space being the power set of the sample space $\Omega$ will not be equal to $\Omega$.
The definition of the sample space in statistics is the set of all possible outcomes of a given trial. In other words, when rolling a single six-sided die, the possible outcomes are the numbers ...
Given a bag of 5 different colour marbles: R, G, B, W, Y, we need to create a sample space to study the outcome of when 3 marbles are picked out of the five marbles in the bag. The way I approached this, is that since we are creating a sample space for 3 marbles picked out of 5, then there is 5 choose 3 ways to make the selection.
As we learned, sample space is the number of possible outcomes of an experiment or study and is used to help find the probability of a specific event (with a specific event being a certain outcome ...
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.
My raw understanding of a sample space is: A set of outcomes from a experiment. Event is a subset of that sample space. And now introduces the definition of conditional event(or worse conditional probability). Consider this problem: The probability of a flawed product in a company is 10%. We have a machine that can detect a product's quality.
If the sample space is all possibilities of two six-sided dice, then there are a total of $6^2$ combinations. Then, you want to know how many outcomes have at least a single $4$ in the
The sample space doesn't have much to do with the probabilities. There are $8$ possible outcomes when flipping a coin three times, so the sample space consists of $8$ individual points and has no real area. The probability comes into play from assigning probabilities to these points (or to events, in a more advanced setting).
To address your edit about expected values, I would say that is probably the only major difference between a finite sample space and a countable one: A finite random variable on a finite sample space always have a well-defined and finite expected value, while a finite random variable on a countably infinite sample space may not have a well-defined expected value.