Probability Density Function of two Resistors in Parallel

Click For Summary
SUMMARY

The discussion centers on calculating the probability density function (PDF) of the equivalent resistance (Z) for two resistors (R1 and R2) in parallel, where R1 = X and R2 = Y are independent random variables uniformly distributed between 100 and 120. The equivalent resistance is defined as Z = XY/(X+Y) or Z = 1/(1/X + 1/Y). The user seeks guidance on deriving the PDF of Z, particularly in contrast to using convolution for the sum of random variables.

PREREQUISITES
  • Understanding of probability density functions (PDFs)
  • Familiarity with random variables and their distributions
  • Knowledge of resistor networks and equivalent resistance calculations
  • Basic principles of convolution in probability theory
NEXT STEPS
  • Study the derivation of the probability density function for functions of random variables
  • Learn about the transformation techniques for random variables
  • Explore the concept of convolution in probability and its applications
  • Investigate the properties of uniform distributions and their implications in circuit analysis
USEFUL FOR

Electrical engineers, statisticians, and students studying probability theory and circuit analysis will benefit from this discussion, particularly those interested in the statistical behavior of resistive networks.

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?
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
2K
Replies
4
Views
3K
  • · Replies 19 ·
Replies
19
Views
5K
Replies
2
Views
2K
  • · Replies 29 ·
Replies
29
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 15 ·
Replies
15
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K