Probability Density Function of two Resistors in Parallel

AI Thread Summary
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
Messages
4
Reaction score
0
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?
 
Engineering news on Phys.org
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?
 
Thread 'Weird near-field phenomenon I get in my EM simulation'

Thread 'Weird near-field phenomenon I get in my EM simulation'

I recently made a basic simulation of wire antennas and I am not sure if the near field in my simulation is modeled correctly. One of the things that worry me is the fact that sometimes I see in my simulation "movements" in the near field that seems to be faster than the speed of wave propagation I defined (the speed of light in the simulation). Specifically I see "nodes" of low amplitude in the E field that are quickly "emitted" from the antenna and then slow down as they approach the far...
View full post »

Thread '3-terminal device external modeling'

Very basic question. Consider a 3-terminal device with terminals say A,B,C. Kirchhoff Current Law (KCL) and Kirchhoff Voltage Law (KVL) establish two relationships between the 3 currents entering the terminals and the 3 terminal's voltage pairs respectively. So we have 2 equations in 6 unknowns. To proceed further we need two more (independent) equations in order to solve the circuit the 3-terminal device is connected to (basically one treats such a device as an unbalanced two-port...
View full post »

Similar threads

Calculating Input/Output Impedance w/ Parallel Resistors
Replies
7
Views
2K
A Probability Density Function: Converting Experimental Observations to PDF
Replies
4
Views
2K
Probability density function of Z=X+Y and Z=XY
Replies
19
Views
4K
Finding Probability Density Functions for Independent Random Variables
Replies
2
Views
2K
Types of circuits that have a nonlinear response to R
Replies
29
Views
2K
A Constructing PDFs for Max Likelihood Density Estimation Problem
Replies
2
Views
2K
B Expectation of probability density function
Replies
3
Views
2K
I Calculating the inverse of a function involving the error function
Replies
3
Views
2K
Resistor parallel to short circuit when finding R_thev ....?
Replies
6
Views
6K
Electrical Circuits - Parallel vs. Series
Replies
14
Views
1K

Hot Threads

Recent Insights

Back
Top