1. The problem statement, all variables and given/known data The lifetime of batteries are independent random variables Xi, i= 1,2,... each having exponential distribution given by the density f(x) = 2e^-2x, x>0, 0 elsewhere. If a flashlight needs two batteries to work, then the time that the flashlight can operate is a random variable Y=min(X1,X2). Find the CDF and PDF of Y 2. Relevant equations Xi, i= 1,2,... Xi ~ f(x) = 2e^-2x, x>0, 0 elsewhere Y=min(X1,X2) 3. The attempt at a solution What i'm not sure about is the initial approach to this problem. I'm not sure if I should treat it as an order statistics problem in which case i'd be trying to use the equation: g(y) = n((1-Fx(y))^(n-1))f(y) though i'm not sure if Fx(y) and f(y) are just the respective cdf and pdf of X. I know if i have the pdf, I can get the cdf easily.