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 of the sort 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 $N$ be the random variable counting the number of even rolls in each outcome. For example, if the outcome is eee, then $N(ee))3.$ Suppose that the random variable $x$ is defined in terms of $N$ as follows: $x=2N^2-6N-1.$ The values of $x$ are given in the table below.

$\backslash$table$[[$Outcome eoe,oeo,eoo,oee,eee,eeo,ooe,ooo,$],[$Value of $x,-5,-5,-5,-5,-1,-5,-5,-1]]$

Calculate the probabilities $P(x=x)$ of the probability distribution of $x.$ First, fill in the first row with the values of $x.$ Then fill in the appropriate probabilities in the second row.