We are tasked with finding $P(X > 7)$, which is the probability that $X$ takes on a value greater than 7. From the given dataWe are tasked with finding $P(X > 7)$, which is the probability that $X$ takes on a value greater than 7. From the given

$x = \{4, 5, 6, 7, 8\}$ $P(X = x) = \{0.1, 0.1, 0.2, 0.2, 0.4\}$

We need to sum the probabilities for all values of $X$ greater than 7, which in this case is only $X = 8$.

$P(X > 7) = P(X = 8) = 0.4$

Thus, the value of $P(X > 7)$ is 0.4.

Do you need more details on probability distributions or have any questions?

Here are five related questions to expand on this topic:

1. How do you find the probability of $P(X < 6)$?
2. What is the sum of all probabilities for $P(X = x)$?
3. How can you verify that the probability distribution is valid?
4. What is the expected value of $X$ for the given data?
5. How would you calculate the variance of this probability distribution?

Tip: The sum of probabilities in any probability distribution must always equal 1.