Probability distribution

A probability distribution in the sample space $S$ is a function $p$ assigning a number $p(s_i)$ to each possible outcome $s_i$ in $S$ (the probability of $s_i$), such that:

• values are exhaustive (cover everything)
• values are mutually exclusive (no overlap)
• $0\le p(s_i)\le 1$, for all $i=1\text{ to }n$
• $p(s_1)+p(s_2)+...+p(s_n)=1$ All probability values add up to $1$.

$$P(\text{Weather})=\left(\begin{array}{c}0.72\\ 0.1\\ 0.08\\ 0.1\end{array}\right)=⟨0.72,0.1,0.08,0.1⟩$$

This means, for example: $P(\text{Weather}=sunny)=0.72$.