Chapter 12.3, Problem 12E

(a)

To determine

To calculate: The expected value $\text{E}\left(X\right)$ and interpret it, whena random variable $X$ denotes the time(in minutes) required to complete an assembly on a production linewith thecumulative distribution functionis $F\left(x\right)=\frac{1}{125}{x}^3,0\le x\le 5$.

(b)

To determine

To calculate: The variance $\text{Var}\left(X\right)$, when a random variable $X$ denotes the time (in minutes) required to complete an assembly on a production line with the cumulative distribution function is $F\left(x\right)=\frac{1}{125}{x}^3,0\le x\le 5$.