Lifetime Distribution of a parallel system (exponential)

[realfunboy]

Suppose under normal operating conditions the operating time in days until failure of a certain type of component has an exponential distribution with mean Lamda(> 0). Suppose a system comprising of three such components works if at least one of the components works. You may assume that the random variables representing lifetimes of different components in the system to be independent.

(i)Find the life time distribution of the system.
(ii)Without finding the mean prove that the mean life time of the system is at least as large as that of a single component
(iii)Prove (ii) if mean is replaced by median
(iv)Find the variance of the life time of the system and compare it with that of a single component.


I ve got the answer to (i). But m stuck wid the rest.

Can someone pls help me to approach parts ii, iii and iv ?


Thanks in advance

 

[royhaas]

The system fails iff all three systems fail.