State which of the following is a probability distributions of a random variable. Give reasons for your answer.

Question

$(i)\quad \begin{matrix} \textbf{X} & 0 &1 &2 \\ \textbf{P(X)} &0.4 &0.4 & 0.2 \end{matrix} \qquad (ii)\quad \begin{matrix} \textbf{X} &0 &1 &2 &3 &4 \\ \textbf{P(X)}&0.1 &0.5 &0.2 &-0.1 &0.3 \end{matrix}$ $(iii)\quad \begin{matrix} \textbf{Y} & -1 &0 &1 \\ \textbf{P(Y)} &0.6 &0.1 & 0.2 \end{matrix} \qquad (iv)\quad \begin{matrix} \textbf{Z} &3 &2 &1 &0 &-1 \\ \textbf{P(Z)}&0.3 &0.2 &0.4 &0.1 &0.05 \end{matrix}$