Problem

Calculate the expected value of the scenario.
Itranscript
\begin{tabular}{|c|c|}
\hline $\mathbf{x}_{\mathbf{i}}$ & $\mathbf{P}\left(\mathbf{x}_{\mathbf{i}}\right)$ \\
\hline 1 & 0.24 \\
\hline 2 & 0.31 \\
\hline 3 & 0.01 \\
\hline 4 & 0.15 \\
\hline 5 & 0.29 \\
\hline
\end{tabular}

Answer
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Expected value $=$

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Answer

The final answer is \( \boxed{2.94} \).

Steps

Step 1 :Calculate the expected value by multiplying each outcome by its probability and summing up the results.

Step 2 :Let the outcomes be \( x_i = [1, 2, 3, 4, 5] \) and the corresponding probabilities be \( P(x_i) = [0.24, 0.31, 0.01, 0.15, 0.29] \).

Step 3 :Compute the expected value using the formula \( \text{Expected value} = \sum_{i=1}^{n} x_i \cdot P(x_i) \).

Step 4 :Substitute the values into the formula to get \( \text{Expected value} = 1 \cdot 0.24 + 2 \cdot 0.31 + 3 \cdot 0.01 + 4 \cdot 0.15 + 5 \cdot 0.29 \).

Step 5 :Calculate the sum to get the expected value \( \text{Expected value} = 2.94 \).

Step 6 :The final answer is \( \boxed{2.94} \).

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