Suppose the time X a customer must spend waiting in line at a certain fast food restaurant is a random variable that is exponentially distributed with a density function $f ( x ) = \left\{ \begin{array} { l l }
\frac { 1 } { 3 } e ^ { - x / 3 } & \text { if } x \geq 0 \
0 & \text { if } x

Question

Suppose the time X a customer must spend waiting in line at a certain fast food restaurant is a random variable that is exponentially distributed with a density function $f ( x ) = \left\{ \begin{array} { l l } 
\frac { 1 } { 3 } e ^ { - x / 3 } & \text { if } x \geq 0 \
0 & \text { if } x < 0
\end{array} \right.$ where x is the number of minutes that a randomly selected customer spends waiting in line.Find the expected waiting time for customers at the restaurant.
A)6 minutes
B)2.5 minutes
C)3 minutes
D)1.5 minutes

Quizplus · Accepted Answer

The expected waiting time for an exponentially distributed random variable is given by $E(X) = \frac{1}{\lambda}$, where $\lambda$ is the rate parameter of the distribution. In this case, the rate parameter $\lambda$ is given as $\frac{1}{3}$, so the expected waiting time is $E(X) = \frac{1}{\frac{1}{3}} = 3$ minutes.

Suppose the Time X a Customer Must Spend Waiting in Line