申論題

5. Suppose that the lifetimes of two components are independent of one another and that the first lifetime,X₁, has an exponential distribution with parameter λ₁, whereas the second, X₂ has an exponential distribution with parameter λ₂.

(b) Let λ₁ = and λ₂ =, so that the expected lifetimes are 1000 hours and 1200 hours,
respectively. The probability that both component lifetimes are at least 1500 hours is __(H)__.