To determine if the table represents a proper discrete probability distribution, we need to check two key conditions:

1. All probabilities must be between 0 and 1: Each value in the $P(x)$ column must lie in the range $[0, 1]$.
2. The sum of all probabilities must equal 1: The sum of all $P(x)$ values must add up to exactly 1.

Given table:

• $x = \{0, 1, 2, 3, 4, 5\}$
• $P(x) = \{0.05, 0.4, 0.04, 0.06, 0.6, 0.01\}$

Step 1: Check if all probabilities are between 0 and 1

• $0.05, 0.4, 0.04, 0.06, 0.6, 0.01$ are all between 0 and 1. ✅

Step 2: Check if the sum of probabilities equals 1

• $0.05 + 0.4 + 0.04 + 0.06 + 0.6 + 0.01 = 1.16$

Since the sum of the probabilities is 1.16, which is greater than 1, this is not a proper discrete probability distribution.

Answer: False

Would you like further details on this?

Here are 5 follow-up questions you might find useful:

1. What are the properties of a valid probability distribution?
2. How can you fix an invalid probability distribution like the one given?
3. What is the difference between discrete and continuous probability distributions?
4. How do you calculate the expected value of a discrete probability distribution?
5. What are some common mistakes when working with probability distributions?

Tip: Always double-check the sum of probabilities when determining if a distribution is valid!