This table represents a probability distribution for the random variable $X$, where the probabilities for each value of $X$ are provided, except for one missing value, denoted as $y$.

The rule for a probability distribution is that the sum of all the probabilities must equal 1. We can use this rule to find $y$.

The equation is:

$0.1 + 0.3 + y + 0.2 + 0.1 = 1$

Simplifying:

$0.7 + y = 1$

So,

$y = 1 - 0.7 = 0.3$

Thus, the missing value $y = 0.3$.

Would you like further details, or do you have any questions? Here are some related questions:

1. How can we verify that this is a valid probability distribution?
2. What is the expected value $E(X)$ for this distribution?
3. What is the variance of $X$ for this distribution?
4. How does one find the cumulative distribution function (CDF) for this type of problem?
5. Can this distribution be classified under a specific type of discrete probability distribution?

Tip: Always check that the sum of probabilities in any probability distribution equals 1 to ensure its validity.