How Do You Calculate P{S < t < S + R} for Independent Exponential Variables?

[motherh]

Hi, I have a quick question.

Let R and S be two independent exponentially distributed random variables with rates λ and μ. How would I compute P{S < t < S + R}?

I am a little bit confused because of the variables on either side of the inequalities. I have tried conditioning on both S and R but I am not sure if I'm doing it right here. I can compute something like P{S < R} but the t is throwing me off!

Any help is appreciated!

 

[Stephen Tashi]

. I can compute something like P{S < R}

Then can't you compute the probability that U < R where U = t - S ?