Determine whether the distribution represents a probability...

Determine whether the distribution represents a probability distribution. If it does not, state why.
$$
\begin{array}{l|ccccc}
\boldsymbol{x} & -5 & -3 & 0 & 2 & 4 \\
\hline \boldsymbol{P}(\boldsymbol{X}) & 0.1 & 0.3 & 0.2 & 0.3 & 0.1
\end{array}
$$

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Key Concepts

Probability Distribution

A probability distribution represents the set of all possible outcomes of a random variable along with their associated probabilities. It must satisfy fundamental axioms such as non-negativity and the total probability summing to 1, ensuring that it accurately reflects a complete and valid model of uncertainty.

Normalization Condition

The normalization condition is the requirement that the sum of the probabilities of all possible outcomes equals 1. This is critical because it guarantees that the probability framework accounts for every possible event, thereby ensuring that one of the outcomes must occur.

Non-Negativity

Non-negativity is a core principle of probability distributions, stating that each probability assigned to an outcome must be zero or positive. This principle is essential since it is impossible to have a negative likelihood for any outcome in a properly defined probability model.

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