An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string like "oee" (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll).

For each outcome, let [tex]$N$[/tex] be the random variable counting the number of even rolls in each outcome. For example, if the outcome is "eee," then [tex]$N(\text{eee}) = 3$[/tex]. Suppose that the random variable [tex]$X$[/tex] is defined in terms of [tex]$N$[/tex] as follows:
[tex]\[ X = 2N - 2N^2 - 3 \][/tex]

The values of [tex]$X$[/tex] are given in the table below.
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline Outcome & oee & eeo & ooe & oeo & eee & ooo & eoe & eoo \\
\hline Value of $X$ & -7 & -7 & -3 & -3 & -15 & -3 & -7 & -3 \\
\hline
\end{tabular}
\][/tex]

Calculate the probabilities [tex]$P(X=x)$[/tex] of the probability distribution of [tex]$X$[/tex]. First, fill in the first row with the values of [tex]$X$[/tex]. Then fill in the appropriate probabilities in the second row.
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline Value $x$ of $X$ & $\square$ & $\square$ & $\square$ \\
\hline $P(X=x)$ & $\square$ & $\square$ & $\square$ \\
\hline
\end{tabular}
\][/tex]