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 How to enter your answer (opens in new window) Expected value $=$

Solution

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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Source: https://solvelyapp.com/problems/zng1ex9Fzl/

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