# Thread: Distribution of time that a flashlight can operate

1. ## Distribution of time that a flashlight can operate

I am wondering if I can get help on the following problem:
If we have a stock of n batteries, each has a lifetime that is exponential
with parameter c and they are independent of each other.
If a flashlight needs 2 batteries, what is the lifetime that the flashlight can operate?
I have 2 solutions that I can think of:
1) The lifetime of the minimum (X,...Xn).
2) The lifetime of the min(Xi,Xj) multiply by all possible pairs, 2 choose n.
Any suggestion???

2. Originally Posted by thomas_donald
I am wondering if I can get help on the following problem:
If we have a stock of n batteries, each has a lifetime that is exponential
with parameter c and they are independent of each other.
If a flashlight needs 2 batteries, what is the lifetime that the flashlight can operate?
I have 2 solutions that I can think of:
1) The lifetime of the minimum (X,...Xn).
2) The lifetime of the min(Xi,Xj) multiply by all possible pairs, 2 choose n.
Any suggestion???
Do you mean "... what is the minimum possible lifetime that the flashlight can operate?" Then it will be minimum (X,...Xn).

3. Sorry for the late response. Thank you very much for your help.