Derived RVs. Suppose you are running a simulation on a large data set. Assuming that the task is parallelizable, you can split it into two component tasks and assign them to two worker nodes and run in parallel. The time for completion at each worker node can be modelled as random variables X and Y respectively where X and Y are two independent exponential random variables with parameters A1 and A2 respectively. Let the random variable Z be defined as the time for completion of the task. Find the CDF and PDF of Z.

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