An engineering system consisting of three components is configured as a series system. The components are acting independently of each other with the ith component's lifetime $T_{i}$ having an exponential distribution with rate $\lambda_{i}$, where $\lambda_{1}=.01,\lambda_{2}=.02,\lambda_{3}=.03$. Since the system is a series system, then the system life is $S=min\{T_{1},T_{2},T_{3}\}$. Find the distribution function and density function of the system life S, and then find its mean and variance.
Alright, so I honestly have no clue how to do this problem. I know that if one component fails then the entire system fails. Can anyone just give me a little hint to get started?
