Find the mean of the following probability distribution? Round your answer to one decimal.
0	0.2679
1	0.1986
2	0.0079
3	0.3987
4	0.1269

mean =

The formula to calculate the mean (expected value) of a probability distribution is:

\[
\text{Mean} = \sum (x \cdot P(x))
\]

where \(x\) represents the values, and \(P(x)\) represents the probabilities.

Given the dataThe formula to calculate the mean (expected value) of a probability distribution is:

\[
\text{Mean} = \sum (x \cdot P(x))
\]

where \(x\) represents the values, and \(P(x)\) represents the probabilities.

Given the 

\[
\text{Mean} = (0 \cdot 0.2679) + (1 \cdot 0.1986) + (2 \cdot 0.0079) + (3 \cdot 0.3987) + (4 \cdot 0.1269)
\]

Let me calculate this for you.

\[
\text{Mean} = (0) + (1 \cdot 0.1986) + (2 \cdot 0.0079) + (3 \cdot 0.3987) + (4 \cdot 0.1269)
\]

\[
\text{Mean} = 0 + 0.1986 + 0.0158 + 1.1961 + 0.5076
\]

Now, summing these values:

\[
\text{Mean} = 0.1986 + 0.0158 + 1.1961 + 0.5076 = 1.9181
\]

Thus, the mean of the probability distribution, rounded to one decimal, is:

\[
\boxed{1.9}
\]

Would you like more details or have any questions?

### Related questions:
1. How do you calculate the variance of a probability distribution?
2. What is the formula for standard deviation in probability distributions?
3. How does the mean differ in a normal distribution versus a skewed distribution?
4. What role does the mean play in the law of large numbers?
5. Can probability distributions have more than one mean value?

### Tip:
The mean of a probability distribution gives the expected outcome over the long term if you repeat the random process multiple times.

Find the mean of the following probability distribution? Round your answer to one decimal.
0 0.2679
1 0.1986
2 0.0079
3 0.3987
4 0.1269
mean =

Learn how to find the mean of a probability distribution with the values 0, 1, 2, 3, and 4, and their respective probabilities. Follow a detailed solution to calculate the expected value using the formula Σ(x * P(x)). Ideal for students in Grades 9-12.

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