Two signals are transmitted through a processor. The transmission times are independent

random variables X1 and X2 with exponential distributions with respective parameters 1 > 0

and 2 > 0, with 1 < 2. It takes the processor an amount T of time to transmit both signals.

Find the density function fT (t) of the variable T, its expected value E(T), its variance Var(T),

and its hazard rate function rT (t), and compute limt!1 rT (t) in the following two cases:

(a) (10 marks) the signals are transmitted sequentially, that is the second signal can be

transmitted only after the rst signal has been transmitted (i.e. T = X1 + X2);

(b) (10 marks) the signals are transmitted simultaneously (i.e. T = max(X1;X2)).