To find $P(X > -4)$, we need to calculate the probability that $X$ takes a value greater than $-4$.

Given the values of $x$ and the corresponding probabilities $P(X=x)$:

• $P(X=-5) = 0.2$
• $P(X=-4) = 0.3$
• $P(X=-3) = 0.2$
• $P(X=-2) = 0.1$
• $P(X=-1) = 0.2$

For $X > -4$, this means $X$ can be $-3, -2, -1$. So, we need to sum the probabilities for $X = -3, -2, -1$:

$P(X > -4) = P(X = -3) + P(X = -2) + P(X = -1)$

Substitute the given values:

$P(X > -4) = 0.2 + 0.1 + 0.2 = 0.5$

So, the value of $P(X > -4)$ is $\mathbf{0.5}$.

Let me know if you'd like more details or if you have any other questions!

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Here are some related questions you might find interesting:

1. How do we interpret the sum of probabilities in a probability distribution?
2. How can we find $P(X \leq -3)$ for the given distribution?
3. What is the condition for a valid probability distribution?
4. What does it mean when the sum of all probabilities in a distribution equals 1?
5. How can we calculate the expected value of $X$ from the given data?

Tip: Always check that the sum of all probabilities in a distribution is 1 to ensure it's valid.