Let X₁, X₂ be independent random variables representing lifetimes in hours) of two key components of a device that fails when and only when both components fail. Say each Xi has an exponential distribution with mean 1000. Let Y₁ = min(X₁, X₂) and Y₂ = max(X₁, X₂), so that the support of Y₁, Y₂ is 0) < y₁ < y₂ < . Compute the probability that the no components fail after 800 hours; that is, compute P(Y₁ > 800).
