Find the mean, , of this probability distribution.

P()
0	0.15
1	0.1
2	0.1
3	0.65


 = 

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

\[
\mu = \sum_{x} x \cdot P(x)
\]

Where:
- \(x\) is a value in the distribution
- \(P(x)\) is the probability associated with that value

Given the distribution:

\[
\begin{array}{c|c}
x & P(x) \\
\hline
0 & 0.15 \\
1 & 0.10 \\
2 & 0.10 \\
3 & 0.65 \\
\end{array}
\]

Now, calculate the mean:

\[
\mu = (0 \times 0.15) + (1 \times 0.10) + (2 \times 0.10) + (3 \times 0.65)
\]

\[
\mu = 0 + 0.10 + 0.20 + 1.95 = 2.25
\]

So, the mean \(\mu\) of the probability distribution is \(2.25\).

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do you calculate the variance of a probability distribution?
2. What is the difference between the mean and the expected value in a probability distribution?
3. How do you interpret the mean of a probability distribution?
4. How would the mean change if the probabilities were different?
5. What role does the mean play in determining the shape of a distribution?

**Tip:** The mean of a probability distribution is also called the expected value, which represents the average outcome you'd expect if you were to repeat an experiment many times.

Find the mean, μ, of this probability distribution:

P(x)
0 - 0.15
1 - 0.1
2 - 0.1
3 - 0.65

μ =

Learn how to calculate the mean (expected value) of a probability distribution with given P(x) values. This problem covers core probability concepts and utilizes the formula μ = Σ(x * P(x)). Suitable for students in Grades 9-11.

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