# Sample Space Random Variable

Is it true that the set of all possible values of a random variable form the sample space?

I think it is false because it is all possible outcomes that form the same space but I wanted to clarify this.

• No, the sample space is where eat a random variable, not the value it takes. – user657324 Apr 9 '19 at 8:19

The sample space is the set of all possible outcomes. For example, if we are flipping a coin the sample space is $$\{H, T\}$$ where $$H$$ is heads and $$T$$ is tails. A random variable is a function from the sample space to the real numbers. For example, we could define the random variable $$X$$ such that $$X(H) = 0$$ and $$X(T) = 1$$. Note there are infinitely many ways that we can make random variables.