Chapter 12.3, Problem 9E

(a)

To determine

The cumulative distribution function of $X$ with the beta probability density

$f\left(x\right)=30x^2{\left(1-x\right)}^2,0\le x\le 1$.

(b)

To determine

To calculate: The probability that less than $25\%$ of the newspaper’s space on a given day contains advertising.

(c)

To determine

To calculate: The expected value $\text{E}\left(X\right)$ and interpret it, when the beta probability density function is $f\left(x\right)=30x^2{\left(1-x\right)}^2,0\le x\le 1$.

(d)

To determine

To calculate: The variance $\text{Var}\left(X\right)$, when the beta probability density functionis $f\left(x\right)=30x^2{\left(1-x\right)}^2,0\le x\le 1$.