Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value $\text{E}\left(X\right)$ and interpret it, whenrandom variable $X$ denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis $F\left(x\right)=\frac{1}{9}{x}^2,0\le x\le 3$.

(b)

To determine

To calculate: The variance $\text{Var}\left(X\right)$, when a random variable $X$ denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function $F\left(x\right)=\frac{1}{9}{x}^2,0\le x\le 3$.