The random variable [math]X[/math] has a distribution with the following density function:

[[math]] f_X(x) = \begin{cases} \theta^{-1} e^{-x/\theta} \,\, x\geq 0 \\ 0 \,\, \textrm{otherwise} \end{cases} [[/math]]

where [math]\theta [/math] is unknown. If the median of the distribution equals 250, determine the standard deviation of [math]X[/math].

1. 19
2. 250
3. 300
4. 360.67
5. 365.67