If the continuous RV. X represents the time of failure of a system, that has been put into operation at t = 0, find the conditional density function of X, given that the system has survived upto time...

Extracted text: If the continuous RV. X represents the time of failure of a system, that has been put into operation at t = 0, find the conditional density function of X, given that the system has survived upto time t. Deduce the same when X follows an exponential distribution with parameter A.