Let X Be a Continuous Random Variable with Density Function $f ( X ) = \left\{ \begin{array} { l l } c \cdot e ^ { - c X } & \text { if } x \geq 0 \\0 & \text { otherwise }\end{array} \right.$

Multiple Choice

Let X be a continuous random variable with density function $f ( X ) = \left\{ \begin{array} { l l } c \cdot e ^ { - c X } & \text { if } x \geq 0 \\0 & \text { otherwise }\end{array} \right.$ If the median of this distribution is $\frac { 1 } { 3 }$ , then c is:

A) $\frac { 1 } { 3 }$ $\ln \frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$ $\ln 2$
C) 2 $\ln \frac { 3 } { 2 }$
D) $3 \ln 2$
E) 3
F) $\frac { 1 } { 3 }$
G) $2 \cdot \frac { \ln 3 } { \ln 2 }$
H) 3 $\ln \frac { 1 } { 2 }$