# Distribution of time that a flashlight can operate

• Nov 16th 2009, 06:55 AM
thomas_donald
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???
• Nov 16th 2009, 06:50 PM
mr fantastic
Quote:

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).
• Dec 2nd 2009, 08:20 AM
thomas_donald
Sorry for the late response. Thank you very much for your help.