Chapter 12.3, Problem 15E

(a)

To determine

The cumulative distribution function $F(x)$ with the density function

$f\left(x\right)=\frac{x\left(6-x\right)}{18},3\le x\le 6$.

(b)

To determine

To calculate: Thelikelihood that the electrical work will take less than $500$ worker-hours, where $X$ represents hundred worker- hours.

(c)

To determine

To calculate: The mean time to complete the work, where a random variable $X$ denotes the time required for the electrical work in hundred worker-hours with the density function $f\left(x\right)=\frac{x\left(6-x\right)}{18},3\le x\le 6$.

(d)

To determine

To calculate: The variance $\text{Var}\left(X\right)$, when the density function is $f\left(x\right)=\frac{x\left(6-x\right)}{18},3\le x\le 6$.