15.2.43 One dimensional random variables and their characteristics

Problem: The probability density of the random variable \( X \) has the form: \[ f_{X}(x)=\left\{\begin{array}{lc} (x+a)^{2}, & \text { if }-a \leq x<0 \\ a^{2}-x^{2}, & \text { if } 0 \leq x \leq a \\ 0, & \text { otherwise } \end{array}\right. \] Find: a) the coefficient \( a \); b) probability \( P\{X \in(-0,5 ; 0,75)\} ; \) c) the expected value of \( \mathrm{M}[X] \) d) the distribution function \( f_{X}(x) \).