Suppose the lifetime of a component $T_i$ in hours is uniformly distributed on $[100, 200]$. Components are replaced as soon as one fails and assume that this process has been going on long enough to reach equilibrium.
(a) What is the probability that the current component has been in operation for at least $50$ hours?
(b) What is the probability that the current component will last for at least $50$ hours more?
(c) What is the probability that the total lifetime of the current component will be at least $150$ hours?
(d) Suppose that it is known that the current component has been in operation for exactly $90$ hours. What is the probability that it will last at least $50$ more hours?
I am not sure how to really start this. Intuitively, I would think the answers would be $0.75$ for a), $.75$ for b), $0.50$ for c), and $0.60$ for d)?
Also, how would you do this for an exponential distribution with mean of $150$? In this case I would not know how to approach this.