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Minimum of two exponentials

MediumProbabilityRandom Variables~4m

X∼Exp(2)X\sim\text{Exp}(2) and Y∼Exp(5)Y\sim\text{Exp}(5) are independent. min⁡(X,Y)\min(X,Y) is exponential; what is its rate parameter?

Show hints (2)+
  1. Use P(min > t) = P(X > t)·P(Y > t).
  2. Rates of independent exponentials add for the minimum.

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