Sample Space
Sample Space¶
A lot of this material is inspired by:
Wiki article
Khan academy videos
MIT OCW course
Assume you toss a coin once, the coin can land either as heads or tails. The outcome is unknown before the throw.
Sample Space
The sample space is the possible outcomes of the experiment. For the coin toss experiment, we can denote the sample space as: \(\Omega = \{H, T\}\)
Now,let us consider a slightly advanced example. Our experiment is to roll two die (6-faced die) and note the sum of the numbers on the top side.
The sample space for this example is:
\[\begin{split}
\begin{align*}
S = \{&(1, 1), (1, 2), \dots, (1, 6), \\
&(2, 1), (2, 2), \dots, (2, 6), \\
&\cdots, \cdots, \cdots, \cdots \\
&(6, 1), (6, 2), \dots, (6, 6) \}
\end{align*}
\end{split}\]