Chapter 6, Problem 45RE

Product warranty. Graph the probability density function for Problem 44 over the interval [0, 3], interpret part (B) of Problem 44 geometrically, and describe the geometric representation.

44. Product warranly. A manufacturer warrants a product for parts and labor for 1 year and for parts only for a second year. The time to a failure of the product after it is sold is given by the probability density function

$f\left(t\right)=\{\begin{array}{cc}0.21e^{-0.21t}& \text{if}t\ge 0\\ 0& \text{otherwise}\end{array}$

What is the probability that a buyer chosen at random will have a product failure

(A) During the first year of warranty?

(B) During the second year of warranty?