(Solved): You are given that \( X \) has cdf \( F_{1}(x) \) as shown below: \[ F_{1}(x)=\left\{\begin{array}{ ...

You are given that \( X \) has cdf \( F_{1}(x) \) as shown below: \[ F_{1}(x)=\left\{\begin{array}{ll} 0 & \text { if } x<-25 \\ 0.05+\frac{3(x+25)}{100} & \text { if }-25 \leq x<-15 \\ 0.45 & \text { if }-15 \leq x<-5 \\ 0.65+\frac{(x+5)}{100} & \text { if }-5 \leq x<10 \\ 0.80+0.17\left(\frac{x-10}{20}\right)^{2} & \text { if } 10 \leq x<30 \\ 1 & \text { if } x \geq 30 \end{array}\right. \] Given: \[ g(x)=\min (2 x+3, x-5,10-3 x) \] Calculate : \[ \operatorname{Pr}[-9 \leq g(x) \leq 9)], E[g(x)], \operatorname{Var}[g(x)] \]