# Math Help - exponential distribution

1. ## exponential distribution

suppose a man operates system consisting of 3 machines whose life time can be modeled by a exponential distribution of beta value 5

How do you find the probability that the system will still be operating without any of it's machines burnt for more than 8 hours?

Please help.

2. Originally Posted by ilikec
suppose a man operates system consisting of 3 machines whose life time can be modeled by a exponential distribution of beta value 5

How do you find the probability that the system will still be operating without any of it's machines burnt for more than 8 hours?

Please help.
Are the machines lifetimes independent of each machine? What unit is lifetime measured in? Hours? Are all machines required to be operating in order for the system to operate? If yes to all, then the answer is p^3 where $p = \int_8^{+\infty} f(x) \, dx$.