X,Y are independent draws from a random number generator so that the density of each of X and Y is 1 on the interval [0,1]. How do you compute the density of the random variable Z = X/Y?
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Well this is a very straighforward and mechanical process , you should tell exactly where are you facing problem ? – abkds Dec 11 '13 at 06:19
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http://math.stackexchange.com/a/30966/6179 – Did Dec 11 '13 at 06:41
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This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. – Did Dec 11 '13 at 06:42
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Hi, I apologize for not providing more details. Okay, I think that I need to first obtain the cdf and then differentiate it to obtain the pdf of random variable Z. To find the cdf I need to perform a double integration over the function, however I am having a hard time trying to figure out what the bounds should be. – user115053 Dec 11 '13 at 06:59
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@user115053 $P(X/Y\le z)=P(X\le zY)=\int_0^1dy,P(X\le zy)=\dots$ – Mario Carneiro Dec 11 '13 at 07:44
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Actually one does not "need to first obtain the cdf and then differentiate it to obtain the pdf", as explained in the link I provided above. – Did Dec 13 '13 at 09:08