John has two light bulbs. The lifetime of the first light bulb is an exponential distribution with mean 1000 hours. The lifetime of the second bulb is uniform over the interval [0 2000] hours.
A. What is the probability that the first bulb will function longer than 1000 hours?
B. What is the probability that the first bulb will function less than 1500 hours after being alive for 1000 hours?
C. Assume that the lifetimes of the two light bulbs are independent and they start to light at the same time. What is the probability that the first light bulb will function longer than the second light bulb?
D. What is the expected total lifetime of two light bulbs?
e. what is the probability that the total lifetime of the two bulbs is between 1000 and 2000 hours.
