1. a. The time to failure of a component in an electronic device has an exponential distribution with a median of four hours. b. i. State the probability distribution function of this random variable. (1 Mark) ii. Compute the probability that the component will work without falling for at least five hours. (9 Marks) A box contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected with replacement. i. Find the probability that fewer than 2 of the selected balls are red. (3 Marks) ii. Find the probability that from 5 balls are selected, 2 are red balls, 1 is yellow ball and 2 are blue balls. (3 Marks) iii. Find the probability that the 3'\" ball selected is the yellow ball. (2 Marks) iv. Find the probability that the 15' ball selected is the blue ball. (2 Marks) [Total: 20 Marks]