To complete the probability distribution for the random variable $X$, we need to ensure two conditions for the probabilities:

1. The sum of all probabilities must equal 1.
2. Each probability must be non-negative.

Given the table:

Step 1: Set up the equation for the total sum of probabilities.

The total must sum to 1, so:

$0.10 + 0.18 + P(X=3) + 0.11 + P(X=6) = 1$

Step 2: Solve for the sum of $P(X = 3) + P(X = 6)$.

$0.10 + 0.18 + 0.11 = 0.39$ $P(X = 3) + P(X = 6) = 1 - 0.39 = 0.61$

Step 3: Distribute the remaining probability.

This leaves $P(X = 3) + P(X = 6) = 0.61$. Without further constraints, one possible solution is to assign equal probabilities:

$P(X = 3) = 0.305 \quad \text{and} \quad P(X = 6) = 0.305$

This would create a valid probability distribution.

Would you like more details on how to adjust this or have any specific questions?

Here are 5 follow-up questions related to probability distributions:

1. What is a probability distribution, and how is it defined for discrete variables?
2. How do you verify if a given set of probabilities forms a valid distribution?
3. How can you find the expected value (mean) of a discrete random variable?
4. What is the significance of the variance and standard deviation in probability distributions?
5. How can probability distributions be applied in real-world scenarios, such as decision-making?

Tip: When solving probability questions, always ensure the total sum of probabilities equals 1, and each individual probability must be between 0 and 1.