To determine if the given distribution is a discrete probability distribution, we need to check the following conditions:

1. The sum of all probabilities must be 1.
2. Each probability must be between 0 and 1 (inclusive).

Given the values:

• $x = -3, -2, 5$
• $P(X = -3) = 0.34$
• $P(X = -2) = 0.06$
• $P(X = 5) = 0.22$

Step 1: Sum of the probabilities

We add the probabilities together:

$P(X = -3) + P(X = -2) + P(X = 5) = 0.34 + 0.06 + 0.22 = 0.62$

Since the sum of the probabilities is 0.62, which is less than 1, this does not satisfy the condition for a valid probability distribution.

Step 2: Check each probability

• $P(X = -3) = 0.34$ is between 0 and 1.
• $P(X = -2) = 0.06$ is between 0 and 1.
• $P(X = 5) = 0.22$ is between 0 and 1.

All the individual probabilities are between 0 and 1, which satisfies the second condition.

Conclusion:

The distribution is not a discrete probability distribution because the sum of the probabilities is not equal to 1.

Would you like a more detailed explanation or assistance with another question? Here are some related questions you might find helpful:

1. What happens if the sum of probabilities is greater than 1?
2. How do you adjust the probabilities to make them sum to 1?
3. Can a continuous distribution have the same conditions as a discrete one?
4. What is the role of the sample space in probability distributions?
5. How can you check if a distribution is valid using software or a calculator?

Tip: Always double-check the sum of probabilities in a distribution before concluding whether it’s valid.