Let $\Omega$ be the sample space for an experiment, and, $F$ is the power set of $\Omega$.
If the experiment consists of just one flip of a fair coin, then the outcome is either heads or tails: $\Omega=\{H,T\}$, then $F=\{\emptyset,\{H\},\{T\},\{H, T\}\}$
Why is a null set included in the power set of sample space? What is its significance with regards to this experiment?
Best Answer
Well first of all, the power set includes ALL subsets. The empty set is a subset and thus it is included.
However I don't think this is what you are asking. In the $\sigma$ algebra, why should one include the empty set? Well the $\sigma$ algebra are the sets you know the probability of. The empty set is the event that nothing happens. If you flip a coin, what is the probability that nothing happens? You don't get a head, or a tail, you get nothing. Well obviously the probability is $0$. So you know the probability of this happening, so it should be included in a $\sigma$ algebra.