(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 orutterlywrong?

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# Homework Help: Joint density problem.

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