Answer
(a) $μ=18.694,
σ²=735.96,
σ≈27.13$
(b) $μ=37.172,
σ²=2947.99,
σ≈54.295$
Work Step by Step
(a) Let x, be the random variable of the number of selects, then,
$μ=E(x)=∑xP(x)=23×0.43+4.2×0.44+11.4×0.04+130×0.05+0×0.04=18.694$
$E(x²)=∑x²P(x)=23²×0.43+4.2²×0.44+11.4²×0.04+130²×0.05+0²×0.04=1085.43$
$σ²=V(x)=E(x²)-[E(x)]²=735.96$
$σ=\sqrt σ²=27.13$
(b) Let y, be the random variable of total number of operations, then,
$μ=E(y)=∑yP(y)=46×0.43+8.8×0.44+12×0.04+260×0.05+1×0.04=37.172$
$E(y²)=∑y²P(y)=46²×0.43+8.8²×0.44+12²×0.04+260²×0.05+1²×0.04=4329.75$
$σ²=V(y)=E(y²)-[E(y)]²=2947.99$
$σ=\sqrt σ²=54.295$
