Questions: Consider the following data: x 3 4 5 6 7 P(X=x) 0.2 0.3 0.1 0.2 0.2 Step 1 of 5: Find the expected value E(X). Round your answer to one decimal place.

Solution Steps

The expected value \(E(X)\) of a discrete random variable is calculated using the formula:

\[ E(X) = \sum_{i} x_i \cdot P(X = x_i) \]

Given the data:

\[ \begin{array}{|c|c|c|c|c|c|} \hline x & 3 & 4 & 5 & 6 & 7 \\ \hline P(X=x) & 0.2 & 0.3 & 0.1 & 0.2 & 0.2 \\ \hline \end{array} \]

We calculate \(E(X)\) as follows:

\[ E(X) = 3 \cdot 0.2 + 4 \cdot 0.3 + 5 \cdot 0.1 + 6 \cdot 0.2 + 7 \cdot 0.2 \]

\[ E(X) = 0.6 + 1.2 + 0.5 + 1.2 + 1.4 \]

\[ E(X) = 4.9 \]

Final Answer