Chapter 9.3, Problem 10E

(a)

To determine

To calculate: The expected value for the probability density function, $f\left(x\right)=\frac{3}{4}x\left(2-x\right)$ on the interval $\left[0,2\right]$.

(b)

To determine

To calculate: The variance for the probability density function, $f\left(x\right)=\frac{3}{4}x\left(2-x\right)$ on the interval $\left[0,2\right]$.

(c)

To determine

To calculate: The standard deviation for the probability density function, $f\left(x\right)=\frac{3}{4}x\left(2-x\right)$ on the interval $\left[0,2\right]$.

(d)

To determine

To graph: The probability density function, $f\left(x\right)=\frac{3}{4}x\left(2-x\right)$ on the interval $\left[0,2\right]$ and mark the mean value.