Find the mean, , of this probability distribution.

P()
0	0.15
1	0.1
2	0.1
3	0.65


 = (one decimal places)

To find the mean (\(\mu\)) of a probability distribution, we use the formula:

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

where:
- \(x\) is the value of the random variable.
- \(P(x)\) is the probability associated with \(x\).

Let's calculate the mean using the given values:

\[
\mu = (0 \cdot 0.15) + (1 \cdot 0.1) + (2 \cdot 0.1) + (3 \cdot 0.65)
\]

Now, compute each term:

\[
\mu = (0) + (0.1) + (0.2) + (1.95)
\]

\[
\mu = 2.25
\]

Thus, the mean (\(\mu\)) of this probability distribution is:

\[
\mu = 2.3 \text{ (one decimal place)}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you calculate the variance of this probability distribution?
2. What is the standard deviation of the probability distribution?
3. Can you provide an example of a discrete probability distribution?
4. How do you interpret the mean in a probability distribution?
5. What is the role of the expected value in statistics?

### Tip:
The mean of a probability distribution, also known as the expected value, provides the average outcome if the experiment were repeated many times.

Find the mean, μ, of this probability distribution.

P()
0	0.15
1	0.1
2	0.1
3	0.65

μ = (one decimal place)

Learn how to calculate the mean (expected value) of a probability distribution using the values P(0)=0.15, P(1)=0.1, P(2)=0.1, and P(3)=0.65. This step-by-step guide covers key concepts in probability, including expected value and mean calculation. Suitable for students in Grades 9-12.

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