Chapter 6.2, Problem 21E

Unless stated to the contrary, compute all monetary answers to the nearest dollar.

21. The life expectancy (in years) of a microwave oven is a continuous random variable with probability density function

     $f\left(x\right)=\{\begin{array}{l}2/{(}^{x}ifx\ge 0\\ \begin{array}{cc}0& \text{otherwise}\end{array}\end{array}$

1. (A)  Find the probability that a randomly selected microwave oven lasts at most 6 years.
2. (B)  Find the probability that a randomly selected microwave oven lasts from 6 to 12 years.
3. (C)  Graph y = f(x) for [0, 12] and show the shaded region for part (A).