Problem
Discrete probability distribution: Basic Fill in the $P(X=x)$ values to give a legitimate probability distribution for the discrete random variable $X$, whose possible values are $-5,-4,4,5$, and 6 \begin{tabular}{|c|c|} \hline Value $x$ of $X$ & $P(X=x)$ \\ \hline-5 & $\square$ \\ \hline-4 & $\square$ \\ \hline 4 & 0.29 \\ \hline 5 & 0.30 \\ \hline 6 & 0.21 \\ \hline \end{tabular} Explanation Check
Solution
Step 1 ：The sum of all probabilities in a probability distribution must equal 1. We already know the probabilities for \(X=4,5,6\) which sum up to \(0.29+0.30+0.21=0.80\).
Step 2 ：Therefore, the sum of probabilities for \(X=-5,-4\) must be \(1-0.80=0.20\).
Step 3 ：We can distribute this remaining probability equally among \(X=-5,-4\) for simplicity, but any distribution that sums to \(0.20\) would be valid.
Step 4 ：The probabilities for \(X=-5\) and \(X=-4\) are both \(\boxed{0.10}\).
