It is given that $$pdf(x)=\lambda_1 e^{-\lambda_1 x}$$ for $x\geq0$ and elsewhere it is zero. Next, It is given that $$pdf(y)=\lambda_2 e^{-\lambda_2 y}$$ for $y\geq0$ and elsewhere it is zero. Assume that $x$ and $y$ are i.i.d.I need to find the pdf of $Z=X/Y$. Can someone give me hints or redirect me to some source. I has been a while since I have dealt transformation of random variables.
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1Possible duplicate of CDF of a ratio of exponential variables; Ratio of exponential distributions. – Em. Dec 14 '19 at 02:38
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They are NOT i.i.d. if $\lambda_1\ne\lambda_2.$ Maybe you meant "Assume $X$ and $Y$ are independent." And you should take care to distinguish between $X$ and $x.$ Without doing that, you can't even understand things like $\Pr(X\le x). \qquad$ – Michael Hardy Dec 14 '19 at 03:06