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May 4th, 2017, 09:35 AM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  Finding a cdf
Let U, V be random numbers chosen independently from the interval [0, 1] with uniform distribution. Find the cumulative distribution and density of each of the variables.req ual (b) Y = U − V . Attempt: I used P (Y < or equal to y), I took the positive side of the absolute value and got P (UV < or equal to y). Later I thought about isolating u to get P (U < or equal to y+V). Thus, J figured the cdf would be F (y)=y+V after using a theorem. However, it was wrong. How should I find the correct cdf? 
May 4th, 2017, 11:04 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,982 Thanks: 1027 
you're letting theorems and formulas get in the way of you understanding what's going on. see if you can sketch the area in [0,1]x[0,1] where UV<c, c some constant in [0,1] no formulas... just common sense and an understanding of the absolute value function. 

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