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I'm asked to show that if $X$ and $Y$ are independent exponential random variables with parameter , then has a Beta distribution.
Up to know I had to find the new pdf or df when $Y$ was of the kind $Y=aB + c$ which I understand now. Here a hint is given to use "Law of total probability" which I've only seen in measure theory.
My guess would be to compute using the fact that the df of exponential distribution is . I'm stuck at that step.