Five males with an X-linked genetic disorder have one child each. The random variable $\mathrm{x}$ is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. \begin{tabular}{c|c} \hline $\mathbf{x}$ & $\mathbf{P ( x )}$ \\ \hline 0 & 0.025 \\ \hline 1 & 0.161 \\ \hline 2 & 0.314 \\ \hline 3 & 0.314 \\ \hline 4 & 0.161 \\ \hline 5 & 0.025 \\ \hline \end{tabular} Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, the random variable $x$ is categorical instead of numerical. C. No, the sum of all the probabilities is not equal to 1 . D. No, not every probability is between 0 and 1 inclusive. E. No, the random variable $x$ 's number values are not associated with probabilities.

Step 1 ：Check if the given table satisfies the conditions for a probability distribution. The conditions are: 1. The sum of all probabilities should be equal to 1. 2. Each individual probability should be between 0 and 1 inclusive. 3. The random variable x should be numerical and associated with probabilities.

Step 2 ：Observe the given values: x_values = [0, 1, 2, 3, 4, 5] and probabilities = [0.025, 0.161, 0.314, 0.314, 0.161, 0.025].

Step 3 ：Calculate the sum of all probabilities. The sum of probabilities is 1.0.

Step 4 ：Check if each individual probability is between 0 and 1 inclusive. All probabilities are in the range.

Step 5 ：Check if the random variable x is numerical and associated with probabilities. The random variable x is numerical.

Step 6 ：Based on the observation, the sum of all probabilities is 1, each individual probability is between 0 and 1 inclusive, and the random variable x is numerical and associated with probabilities.

Step 7 ：Conclude that the table does show a probability distribution. Final Answer: \(\boxed{\text{A. Yes, the table shows a probability distribution.}}\)