Chapter 9.3, Problem 48E

(a)

To determine

To calculate: The mean and standard deviation of the given probability density function $f\left(x\right)=\frac{3}{256}\left(x-2\right)\left(10-x\right) \text{with range} \left[2,10\right]$.

(b)

To determine

To calculate: The median of the given probability density function

$f\left(x\right)=\frac{3}{256}\left(x-2\right)\left(10-x\right) \text{with range} \left[2,10\right]$.

(c)

To determine

To calculate: The probability for given probability density function

$f\left(x\right)=\frac{3}{256}\left(x-2\right)\left(10-x\right) \text{with range} \left[2,10\right]$.