The table you've provided represents a discrete probability distribution for the random variable $x$. The values of $x$ range from 0 to 5, with corresponding probabilities $P(x)$ for each value.

Here is the data:

This is a discrete probability distribution, which follows these key properties:

1. The sum of all probabilities should be 1.
2. Each probability is between 0 and 1 (inclusive).

Sum of Probabilities:

$0.10 + 0.41 + 0.19 + 0.15 + 0.10 + 0.05 = 1.00$

Thus, the given distribution is valid.

If you're asked to compute any related questions (such as finding the expected value, variance, or probabilities for certain ranges of $x$), please let me know!

Would you like further details or help with a specific calculation? Here are some related questions:

1. How do you calculate the expected value of this distribution?
2. How do you compute the variance for this distribution?
3. What is the probability that $x$ is greater than 2?
4. Can you explain the concept of a discrete probability distribution in more detail?
5. How would you apply the probability distribution in real-world scenarios?

Tip: Always ensure the sum of the probabilities in a discrete probability distribution equals 1, as it validates the distribution!