(Solved): Problem 2) The random variable \( X \) has the following probability density function: \[ f_{x}(x)= ...

Problem 2) The random variable \( X \) has the following probability density function: \[ f_{x}(x)=\left\{\begin{array}{ll} c x & 0 \leq x \leq 2 \\ 0 & \text { otherwise } \end{array}\right. \] a) Find the constant \( c \). b) Find \( P[0 \leq X \leq 1] \). c) Find \( P[-1 / 2 \leq X \leq 1 / 2] \). d) Find the CDF \( F_{X}(x) \).