- #1

axiomlu

- 2

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- MHB
- Thread starter axiomlu
- Start date

In summary, the conversation discusses the different interpretations of the variable N and its derivative in a mathematical context. The participants discuss the potential meanings of N, including its representation as a probability distribution and its potential abstract nature. They also consider the application of the chain rule to determine the derivative of N.

- #1

axiomlu

- 2

- 0

Physics news on Phys.org

- #2

HallsofIvy

Science Advisor

Homework Helper

- 42,988

- 981

parameters. I don't know what you mean by "[tex]N(a, b, c, d, \rho)[/tex]", with 5 variables. Also, since N reduces to a function in the single variable, you should get [tex]\frac{dN}{dx}[/tex], not [tex]\frac{\partial N}{\partial x}[/tex] but that is a matter of notation, not substance.

In any case, by the "chain rule", [tex]\frac{dN}{dx}= \frac{\partial N}{\partial a}\frac{da}{dx}+ \frac{\partial N}{\partial b}\frac{db}{dx}+ \frac{\partial N}{\partial c}\frac{dc}{dx}+ \frac{\partial N}{\partial d}\frac{dd}{dx}+ \frac{\partial N}{\partial \rho}\frac{d\rho}{dx}[/tex].

Since a= 0.5x+ 3, da/dx= 0.5, b= -2x, db/dx= -2, [tex]c= x^2[/tex], dc/dx= 2x, d= x+ 0.2, dd/dx= 1, [tex]\rho= 0.4x- 0.2[/tex], [tex]d\rho/dx= 0.4[/tex] so

[tex]\frac{dN}{dx}= 0.5\frac{\partial N}{\partial a}- 2\frac{\partial N}{\partial b}+ 2x\frac{\partial N}{\partial c}+ \frac{\partial N}{\partial d}+ 0.4\frac{\partial N}{\partial \rho}[/tex].

In any case, by the "chain rule", [tex]\frac{dN}{dx}= \frac{\partial N}{\partial a}\frac{da}{dx}+ \frac{\partial N}{\partial b}\frac{db}{dx}+ \frac{\partial N}{\partial c}\frac{dc}{dx}+ \frac{\partial N}{\partial d}\frac{dd}{dx}+ \frac{\partial N}{\partial \rho}\frac{d\rho}{dx}[/tex].

Since a= 0.5x+ 3, da/dx= 0.5, b= -2x, db/dx= -2, [tex]c= x^2[/tex], dc/dx= 2x, d= x+ 0.2, dd/dx= 1, [tex]\rho= 0.4x- 0.2[/tex], [tex]d\rho/dx= 0.4[/tex] so

[tex]\frac{dN}{dx}= 0.5\frac{\partial N}{\partial a}- 2\frac{\partial N}{\partial b}+ 2x\frac{\partial N}{\partial c}+ \frac{\partial N}{\partial d}+ 0.4\frac{\partial N}{\partial \rho}[/tex].

- #3

I like Serena

Homework Helper

MHB

- 16,336

- 258

What does $N$ represent?

Normally it would represent a probability distribution, and more specifically the

However, that is not a function that we can take a derivative of.

And it is already clear that it is not the normal distribution, since that one has a single mean and a single variance.

Is it perhaps supposed to represent the probability density function of a distribution?

Or is it supposed to be something abstract. If so, HallsofIvy's response gives the best we can do.

A partial differential to binomial distribution is a mathematical equation that describes the probability of a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success. It is often used in statistics and probability to model real-world scenarios.

A partial differential to binomial distribution takes into account the continuous nature of the variables involved, while a regular binomial distribution only considers discrete variables. This means that a partial differential to binomial distribution can be used to model situations where the number of trials or the probability of success can vary continuously.

The key components of a partial differential to binomial distribution are the number of trials, the probability of success in each trial, and the number of successes. These variables are used to calculate the probability of obtaining a specific number of successes in a given number of trials.

A partial differential to binomial distribution can be calculated using the formula P(x) = (n choose x) * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successes, and p is the probability of success in each trial. This formula is used to calculate the probability of obtaining exactly x successes in n trials.

A partial differential to binomial distribution can be used in various fields, such as finance, biology, and engineering. For example, it can be used to model the probability of a stock price reaching a certain level, the likelihood of a drug being effective in a clinical trial, or the chance of a machine failing during production. It is a versatile tool for analyzing and predicting outcomes in many different scenarios.

- Replies
- 9

- Views
- 1K

- Replies
- 4

- Views
- 1K

- Replies
- 2

- Views
- 1K

- Replies
- 7

- Views
- 1K

- Replies
- 17

- Views
- 2K

- Replies
- 3

- Views
- 1K

- Replies
- 7

- Views
- 1K

- Replies
- 4

- Views
- 2K

- Replies
- 8

- Views
- 2K

Share: