- #1
ja404
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Homework Statement
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
Homework Equations
Xi, i= 1,2,...
Xi ~ f(x) = 2e^-2x, x>0, 0 elsewhere
Y=min(X1,X2)
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.