Let X and Y be independent exponentially distributed random variables with identical probability density functions, i.e.,...

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Let X and Y be independent exponentially distributed random variables with identical probability density functions, i.e., fx(x) = de-A for a > 0, fy (y) = de-v for y > 0, for some A > 0, and zero otherwise. Show that the probability density of a random variable X + Y is given by fx+y(t) = S1?te-, for t>0, for t<0. Let X and Y be independent exponentially distributed random variables with identical probability density functions, i.e., fx(x) = de-A for a > 0, fy (y) = de-v for y > 0, for some A > 0, and zero otherwise. Show that the probability density of a random variable X + Y is given by fx+y(t) = S1?te-, for t>0, for t<0.