Find the expected value of a random variable X having the following probability distribution: $$\begin{array} { c c c c c }
x & 10 & 20 & 30 & 40 \
P ( X = x ) & \frac { 20 } { 50 } & \frac { 10 } { 50 } & \frac { 15 } { 50 } & \frac { 5 } { 50 }
\end{array}$$ Round your answer to tenth if necessary.

A) $E ( X ) = 21$
B) $E ( X ) = 16$
C) $E ( X ) = 25$
D) $E ( X ) = 12.5$
E) $E ( X ) = 10$

Question

Find the expected value of a random variable X having the following probability distribution: $$\begin{array} { c c c c c } 
x & 10 & 20 & 30 & 40 \
P ( X = x ) & \frac { 20 } { 50 } & \frac { 10 } { 50 } & \frac { 15 } { 50 } & \frac { 5 } { 50 }
\end{array}$$   Round your answer to tenth if necessary.
 
A) $E ( X ) = 21$
B) $E ( X ) = 16$
C) $E ( X ) = 25$
D) $E ( X ) = 12.5$
E) $E ( X ) = 10$

Quizplus · Accepted Answer

The expected value $E(X)$ is calculated as $\sum x_i \cdot P(X = x_i)$. So, $E(X) = 10 \cdot \frac{20}{50} + 20 \cdot \frac{10}{50} + 30 \cdot \frac{15}{50} + 40 \cdot \frac{5}{50} = 21$.

Find the Expected Value of a Random Variable X Having