Suppose the length of time that it takes a person to complete a hedgerow maze is measured by a random variable X that is exponentially distributed with a probability density function $$f ( x ) = \left\{ \begin{array} { l l }
\frac { 1 } { 4 } x e ^ { - x / 2 } & \text { if } x \geq 0 \
0 & \text { if } x

Question

Suppose the length of time that it takes a person to complete a hedgerow maze is measured by a random variable X that is exponentially distributed with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 1 } { 4 } x e ^ { - x / 2 } & \text { if } x \geq 0 \
0 & \text { if } x < 0
\end{array} \right.$$ where x is the number of minutes a randomly selected person takes to complete the maze. Find the probability that a randomly chosen person will take less than 4 minutes to complete the maze.

Quizplus · Accepted Answer

The Answer of Suppose the length of time that it takes a person to complete a hedgerow maze is measured by a random variable X that is exponentially distributed with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 1 } { 4 } x e ^ { - x / 2 } & \text { if } x \geq 0 \
0 & \text { if } x < 0
\end{array} \right.$$ where x is the number of minutes a randomly selected person takes to complete the maze. Find the probability that a randomly chosen person will take less than 4 minutes to complete the maze.

Suppose the Length of Time That It Takes a Person f(x)={14xe−x/2 if x≥00 if x<0f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 4 } x e ^ { - x / 2 } & \text { if } x \geq 0 \\0 & \text { if } x < 0\end{array} \right.f(x)={41​xe−x/20​ if x≥0 if x<0​

Suppose the Length of Time That It Takes a Person $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 4 } x e ^ { - x / 2 } & \text { if } x \geq 0 \\0 & \text { if } x < 0\end{array} \right.$