In the following probability distribution, the random variable $x$ represents the number of activities a parent of a $K$ to $5$ th$-$grade student is involved in$.$ Complete parts $($a$)$ through $($f$)$ below.

$\backslash$table$[[x,0,1,2,3,4],[P(x),0\mathrm{.}079,0\mathrm{.}348,0\mathrm{.}287,0\mathrm{.}207,0\mathrm{.}079]]$

$($a$)$ Verify that this is a discrete probability distribution.

This is a discrete probability distribution because the sum of the probabilities is and each probability is