Cumulative distribution function

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The discussion focuses on finding the cumulative distribution function (CDF) for the random variable Z defined as Z = (X + Y) / (X - Y), where X and Y are independent uniform random variables on the interval [0, 1]. Participants highlight that Z cannot take certain values, such as zero or negative numbers, due to the constraints on X and Y. They emphasize the importance of determining the attainable range of Z to correctly formulate the CDF. The conversation also touches on the necessity of understanding the probability density function (PDF) and integrating it to derive the CDF, with suggestions to visualize the function to clarify its behavior. Ultimately, the thread illustrates the complexities involved in deriving the CDF for Z and the significance of identifying valid intervals for integration.
  • #61
ulissess said:
y>\frac{z-1}{z+1}x==>z>\frac{y+x}{x-y}
In other words, your shaded triangle represents Pr(z>Z). That obviously is not the CDF, but it should also be obvious that it is closely related to the CDF. How?
 
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  • #62
i don't understand very well..
 

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