Can the following table be a probability distribution?
1	0.0086
2	0.2971
3	0.1435
4	0.3417
5	0.2091

no
yes

To determine if a table can represent a probability distribution, it must meet two key criteria:

1. **Each probability must be between 0 and 1**, inclusive.
2. **The sum of the probabilities must equal 1**.

Let's check both criteria:

1. All probabilities in the table are between 0 and 1:
   - \(0.0086, 0.2971, 0.1435, 0.3417, 0.2091\) are all within the range \([0, 1]\).
   
2. Sum of the probabilities:
   \[
   0.0086 + 0.2971 + 0.1435 + 0.3417 + 0.2091 = 1
   \]

Since the sum equals 1, **yes**, this can be a probability distribution.

Would you like further details or have any questions?

Here are 5 questions related to this:
1. What are the properties of a probability distribution?
2. Can a probability distribution have negative values?
3. How do you interpret a probability of zero?
4. What is the difference between a discrete and a continuous probability distribution?
5. How do you verify if a set of probabilities is valid?

**Tip**: Always check that the sum of probabilities equals 1 when verifying a probability distribution!

Can the following table be a probability distribution?
1  0.0086
2  0.2971
3  0.1435
4  0.3417
5  0.2091

Learn how to verify if a table can represent a probability distribution by ensuring the sum of the probabilities equals 1. The table contains the values 0.0086, 0.2971, 0.1435, 0.3417, and 0.2091, all within the range [0, 1]. This problem is ideal for students in Grades 10-12, covering key concepts of probability distributions.

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