I have such a question in my exam:
A type of network router has a bandwidth total to first hardware failure called expressed in terabytes. the random variable is modelled by an exponential distribution whose density is given by one of the following function:
() = 1/θ for s ∈ [0, θ] with a single parameter .
Consider the bandwidth total to failure of the sequence of the two routers(one being brought up automatically when the first is broken).
Express in terms of the bandwidth total to failure of single routers 1 and 2. Calculate the density function of the variable .
I understood that the total bandwidth should be the sum of 2 routers' bandwidths, but I am confused with statement 'one being brought up automatically when the first is broken'. Does it mean that the total bandwidth os the minimum of 2 bandwidths? And how to get the pdf of T using transformation theorem?