Find the mean of the given probability distribution. x P(x) 0 0.11 1 0.26 2 0.35 3 0.21 4 0.07 1.87 1.78 1.57 1.68

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**Find the mean of the given probability distribution.**

The table shows the probability distribution of a random variable \(x\):

\[
\begin{array}{|c|c|}
\hline
x & P(x) \\
\hline
0 & 0.11 \\
1 & 0.26 \\
2 & 0.35 \\
3 & 0.21 \\
4 & 0.07 \\
\hline
\end{array}
\]

**Options for the mean:**

- 1.87
- 1.78
- 1.57
- 1.68

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

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

Calculate the mean by multiplying each value of \(x\) by its corresponding probability \(P(x)\), and then summing these products.
Transcribed Image Text:**Find the mean of the given probability distribution.** The table shows the probability distribution of a random variable \(x\): \[ \begin{array}{|c|c|} \hline x & P(x) \\ \hline 0 & 0.11 \\ 1 & 0.26 \\ 2 & 0.35 \\ 3 & 0.21 \\ 4 & 0.07 \\ \hline \end{array} \] **Options for the mean:** - 1.87 - 1.78 - 1.57 - 1.68 To find the mean (\(\mu\)) of a probability distribution, use the formula: \[ \mu = \sum [x \cdot P(x)] \] Calculate the mean by multiplying each value of \(x\) by its corresponding probability \(P(x)\), and then summing these products.
Expert Solution
Step 1
x p(x) x*p(x)
0 0.11 0
1 0.26 0.26
2 0.35 0.70
3 0.21 0.63
4 0.07 0.28
    Σx*p(x) = 1.87
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