1. The length of a continuous nylon filament that can be drawn without a break occurring is an exponential random variable with mean 5000 feet.
(a) What is the probability that the length of a filament chosen at random lies between 4750 and 5550 feet?
(b) Find the 10th percentile of the distribution of filament length.
2. A particular electronic system has three electronic components. Let Ai repre sent the event that component iis functioning. Let P(A1) = 0.4, P( A2 ) = 0.6, and P( A3 ) = 0.5. The events Ai are independent, and at least two compo nents must be functioning in order for the system to function.
(a) In how many different ways can the system be functioning?
(b) What is the probability that the system is functioning?
(c) In how many ways could the system be functioning if there were n components and at least k of them had to function in order for the system to function.