Let X Be a Random Variable That Measures the Age $$f ( x ) = \left\{ \begin{array} { l l } k e ^ { - k x } & \text { for } x \geq 0 \\0 & \text { otherw ise }\end{array} \right.$$

Let X be a random variable that measures the age of a randomly selected virus in a particular population. Suppose X is exponentially distributed with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } k e ^ { - k x } & \text { for } x \geq 0 \\0 & \text { otherw ise }\end{array} \right.$$ where x is the age of a randomly selected virus and k is a positive constant. Experiments indicate that it is four times as likely for a virus to be less than 2 days old as it is for it to be more than 2 days old. Use this information to determine k.