To find the expected value of a random variable given its probabilities and corresponding scores, you can use the formula:
\[ E(X) = \sum (x_i \cdot p_i) \]
where \( x_i \) is the score and \( p_i \) is the probability.
Let's compute the expected value using the provided data:
\[ \begin{align*} E(X) &= (0 \cdot 0.08) + (5 \cdot 0.25) + (7 \cdot 0.08) + (9 \cdot 0.13) + (10 \cdot 0.23) + (14 \cdot 0.23) \ &= (0) + (1.25) + (0.56) + (1.17) + (2.3) + (3.22) \ &= 0 + 1.25 + 0.56 + 1.17 + 2.3 + 3.22 \ &= 8.5 \end{align*} \]
Thus, the expected value of the random variable is \( 8.5 \).