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].

• 19
• 250
• 300
• 361
• 366