Probability: Sums and Products of Random Variablesby dizzle1518 Tags: probability, products, random, sums, variables 

#1
May1111, 05:42 PM

P: 17

1. The problem statement, all variables and given/known data
Suppose that X is uniformly distributed on (0,2), Y is uniformly distributed on (0,3), and X and Y are independent. Determine the distribution functions for the following random variables: a)XY b)XY c)X/Y 3. The attempt at a solution ok so we know the density fx=1/2 and fy=1/3. Since they are independent then fxy(xy)=(1/2)*1/3)=1/6. So we will integrate 1/6 over the rectangle with y (height) 3 and x (width) 2. for a) we have P(XY<=Z) = P(XZ<=Y). This is were I get stuck. I am not sure what my limits of integration are. I know that XY can be no less than 3 (03). and no more than 2 (20). How do I go about finding the limits of integration? Same thing with b and c. For example b yield P(XY<=Z) which is equal to P(Z/X<=Y). So that would be the area of the rectangle under the hyperbola Z/X. 


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