Probability Density Function of two Resistors in Parallel

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To find the probability density function (PDF) of the equivalent resistance Z for two resistors in parallel, where R1 = X and R2 = Y are independent uniform random variables over the range of 100-120, one must first express Z as Z = 1/(1/X + 1/Y). The challenge lies in determining the PDF of Z, as the method of convolution used for the sum of random variables does not apply directly here. A suggested approach involves transforming the variables and using the Jacobian method to find the inverse of X or Y. Understanding the relationship between the resistances and their distributions is crucial for deriving the PDF of Z accurately.
darthhath
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I have a problem where there are two resistors in parallel and I need to find the equivalent resistance. R1 = X and R2 = Y, and X and Y are independent random variables, uniform over the range of 100-120.

If R equivalent = Z = XY/X+Y, what is probability density function of Z?
 
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Z also equals 1/(1/x +1/y) hope this helps..
 
I know how to find Z when it equals X+Y by using convolution, but I don't know how to do it in this case. How do I find the inverse of X or Y?
 
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