https://file.aiquickdraw.com/mathbot/file/1727495002806x8qo016q.jpg

To solve this question, we need to calculate the mean of the given probability distribution.

The mean \( \mu \) of a discrete probability distribution is calculated as:

\[
\mu = \sum X \cdot P(X)
\]

Where \( X \) is the value, and \( P(X) \) is its associated probability.

From the image, the distribution is:

\[
X: 1, 2, 3, 4, 5
\]
\[
P(X): 0.2, 0.2, 0.1, 0.3, 0.2
\]

Now, calculate the mean.

\[
\mu = (1 \cdot 0.2) + (2 \cdot 0.2) + (3 \cdot 0.1) + (4 \cdot 0.3) + (5 \cdot 0.2)
\]

Let me compute that for you.The mean of the given distribution is \( 3.1 \).

Would you like further details or explanations on this?

Here are 5 related questions to expand your understanding:

1. How is the mean of a continuous probability distribution calculated?
2. What is the difference between mean, median, and mode in probability?
3. How do we calculate the variance and standard deviation of a probability distribution?
4. What does the expected value tell us in the context of probability?
5. How can you check if a given probability distribution is valid?

**Tip:** The sum of all probabilities in a distribution must always equal 1.

Consider the following distribution: X = 1, 2, 3, 4, 5 with P(X) = 0.2, 0.2, 0.1, 0.3, 0.2. What is the mean of this distribution?

Learn how to calculate the mean of a discrete probability distribution with X values of 1, 2, 3, 4, 5 and P(X) values of 0.2, 0.2, 0.1, 0.3, 0.2. This solution covers key concepts such as mean and probability distributions, suitable for students in Grades 9-12.

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