Question: The weekly demand is a random variable X with pdf

\[f\left( x \right)=\left\{ \begin{aligned} & k{{e}^{-2x}}\,\,\,\,\,1\le x\le 4 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right.\]

(a) Calculate the cdf of X, \(\Pr \left( 0<X<2.5 \right)\) and \(\Pr \left( X>1.5 \right)\)

(b) Calculate \(E\left( X \right)\), \(\operatorname{var}\left( X \right)\) and the median.