Intelligent Electronics, Inc., manufactures monochrome liquid crystal display (LCD) notebook computer screens. The number of hours an LCD screen functions until failure is represented by the outcome of a random variable \(X\) having range \(R(X)=[0, \infty)\) and PDF

\(f(x)=.01 \exp \left(-\frac{x}{100}ight) I_{[0, \infty)}(x)\).

The value of \(x\) is measured in thousands of hours. The company has a 1 -year warranty on its LCD screen, during which time the LCD screen will be replaced free of charge if it fails to function.

a. Assuming that the LCD screen is used for 8,760 hours per year, what is the probability that the firm will have to perform warranty service on an LCD screen?

b. What is the probability that the screen functions for at least 50,000 hours? Given that the screen has already functioned for 50,000 hours, what is the probability that it will function for at least another 50,000 hours?