Question

Probability Scores
0.08 0
0.25 5
0.08 7
0.13 9
0.23 10
0.23 14


Find the expected value of the above random variable.

Answer 1

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 \( 8.5 \).