(A) Show That Is the Probability Density Function of a Random Variable

Essay

(a) Show that $$f ( x ) = \left\{ \begin{array} { l l } 4 x + 12 x ^ { 2 } & \text { if } 0 \leq x \leq \frac { 1 } { 2 } \\0 & \text { otherwise }\end{array} \right.$$ is the probability density function of a random variable.(b) What is the mean for this distribution?
(c) Calculate the median of $f$