- #1
spitz
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Homework Statement
I have:
[tex]f_A=\lambda e^{-\lambda a}[/tex]
[tex]f_B=\mu e^{-\mu b}[/tex]
([itex]A[/itex] and [itex]B[/itex] are independent)
I need to find the density of [itex]C=\min(A,B)[/itex]
2. The attempt at a solution
[tex]f_C(c)=f_A(c)+f_B(c)-f_A(c)F_B(c)-F_B(c)f_A(c)[/tex]
[tex]=\lambda e^{-\lambda c}+\mu e^{-\mu c}-\lambda e^{-\lambda c}(1-e^{-\mu c})-(1-e^{-\lambda c})\mu e^{-\mu c}[/tex]
[tex]=\lambda e^{-\lambda c}e^{-\mu c}+\mu e^{-\lambda c}e^{-\mu c}[/tex]
[tex]=2(\lambda+\mu)e^{-c(\lambda+\mu)}[/tex]
Correct or utterly wrong?