15.2.30 One dimensional random variables and their characteristics

Problem: The distribution density of the random variable \( \xi \) is given: \[ f_{\xi}(x)=\left\{\begin{array}{c} 0, \text { if } x \leq-4, \\ \frac{c}{16} x+\frac{1}{4}, \text { if }-44 . \end{array}\right. \] The random variable \( \tau \) is equal to: \[ \tau=\left\{\begin{array}{cc} \xi, & \text { if } \xi<0, \\ -\xi, & \text { if } \xi \geq 0 . \end{array}\right. \] Find 1. the constant \( c \). 2. the distribution density and the expected value of the random variable \( \tau \).