Answer
(a) $F(x)=\left\{\begin{array}{ll}{0,} & {X<0} \\ {0.17,} & {0 \leq X<2} \\ {0.52,} & {2 \leq X<3}\\ {0.85,} & {3 \leq X<4} \\ {1,} & {X \geq 4}\end{array}\right.$
(b) $μ=2.29$
$σ²=1.5259$
Work Step by Step
(a) $F(x)=\left\{\begin{array}{ll}{0,} & {X<0} \\ {0.17,} & {0 \leq X<2} \\ {0.17+0.35=0.52,} & {2 \leq X<3}\\ {0.52+0.33=0.85,} & {3 \leq X<4} \\ {1,} & {X \geq 4}\end{array}\right.$
(b) $μ=E(x)=∑xP(x)=0×0.17+2×0.35+3×0.33+4×0.15=2.29$
$E(x²)=∑x²P(x)=0²×0.17+2²×0.35+3²×0.33+4²×0.15=6.77$
$σ²=V(x)=E(x²)-[E(x)]²=1.5259$
