# Probability Density Function of two Resistors in Parallel

• darthhath
In summary, a Probability Density Function (PDF) is a mathematical function that describes the probability distribution of a random variable. It is calculated by finding the product of the individual PDFs of two resistors in parallel, following the multiplication rule of probabilities. The PDF of two resistors in parallel follows the distribution of the individual resistors, and the value of resistors can affect the shape and range of the distribution. Studying the PDF of two resistors in parallel is important in understanding the behavior and performance of electrical circuits and designing more efficient and reliable circuits.
darthhath
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?

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?

## 1. What is a Probability Density Function (PDF)?

A Probability Density Function (PDF) is a mathematical function that describes the probability distribution of a random variable. It shows the likelihood of a specific value or range of values occurring for a given variable.

## 2. How is the PDF of two resistors in parallel calculated?

The PDF of two resistors in parallel can be calculated by finding the product of the individual PDFs of the two resistors. This is because the parallel combination of resistors follows the multiplication rule of probabilities.

## 3. Does the PDF of two resistors in parallel follow a specific distribution?

The PDF of two resistors in parallel follows the distribution of the individual resistors. If the individual resistors have a normal distribution, then the PDF of the parallel combination will also have a normal distribution.

## 4. How does the value of resistors affect the PDF of two resistors in parallel?

The value of resistors can affect the PDF of two resistors in parallel, as it can change the shape and range of the distribution. Lower resistor values tend to result in a narrower and taller PDF, while higher resistor values lead to a wider and shorter PDF.

## 5. What is the significance of studying the PDF of two resistors in parallel?

Studying the PDF of two resistors in parallel is significant in understanding the behavior and performance of electrical circuits. It helps in predicting the probability of certain values occurring and can aid in designing more efficient and reliable circuits.

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