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I have:

$f_A=\lambda e^{-\lambda a}$

$f_B=\mu e^{-\mu b}$

I need to find the density for $C=\min(A,B)$

($A$ and $B$ are

Is this correct or

$f_C(c)=f_A(c)+f_B(c)-f_A(c)F_B(c)-F_A(c)f_B(c)$

$=\lambda e^{-\lambda c}+\mu e^{-\mu c}-\lambda e^{-\lambda c}(1-e^{-\mu c})-(1-e^{-\lambda c})\mu e^{-\mu c}$

$=\lambda e^{-\lambda c}e^{-\mu c}+\mu e^{-\lambda c}e^{-\mu c}$

$=2(\lambda+\mu)e^{-c(\lambda+\mu)}$

$f_A=\lambda e^{-\lambda a}$

$f_B=\mu e^{-\mu b}$

I need to find the density for $C=\min(A,B)$

($A$ and $B$ are

**independent**).Is this correct or

*utterly*wrong?$f_C(c)=f_A(c)+f_B(c)-f_A(c)F_B(c)-F_A(c)f_B(c)$

$=\lambda e^{-\lambda c}+\mu e^{-\mu c}-\lambda e^{-\lambda c}(1-e^{-\mu c})-(1-e^{-\lambda c})\mu e^{-\mu c}$

$=\lambda e^{-\lambda c}e^{-\mu c}+\mu e^{-\lambda c}e^{-\mu c}$

$=2(\lambda+\mu)e^{-c(\lambda+\mu)}$

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