Recent questions in Expected Value Formula

High school probabilityAnswered question

Israel Young 2023-03-19

The value of $(243{)}^{-\frac{2}{5}}$ is _______.

A)9

B)$\frac{1}{9}$

C)$\frac{1}{3}$

D)0

A)9

B)$\frac{1}{9}$

C)$\frac{1}{3}$

D)0

High school probabilityAnswered question

Lizeth Herring 2022-12-30

If x varies directly as a square of y for y=6, x=72. Find x for y=9.

High school probabilityAnswered question

kokoszzm 2022-06-27

I found in many places that the average momentum of a particle is given by:

$\u27e8p\u27e9={\int}_{-\mathrm{\infty}}^{\mathrm{\infty}}{\psi}^{\ast}\left(\frac{\hslash}{i}\right)\frac{\mathrm{\partial}\psi}{\mathrm{\partial}x}\phantom{\rule{mediummathspace}{0ex}}\mathrm{d}x$

I think that it comes from considering the classical momentum:

$\u27e8p\u27e9=m\frac{\mathrm{d}\u27e8x\u27e9}{\mathrm{d}t}$

and that the expected value of the position is given by:

$\u27e8x\u27e9={\int}_{-\mathrm{\infty}}^{\mathrm{\infty}}x\phantom{\rule{mediummathspace}{0ex}}{|\psi (x,t)|}^{2}\phantom{\rule{mediummathspace}{0ex}}\mathrm{d}x$

But when replacing $\u27e8x\u27e9$ and differentiating inside the integral I don't know how to handle the derivatives of $\psi $ for getting the average momentum formula. Any suggestion?

$\u27e8p\u27e9={\int}_{-\mathrm{\infty}}^{\mathrm{\infty}}{\psi}^{\ast}\left(\frac{\hslash}{i}\right)\frac{\mathrm{\partial}\psi}{\mathrm{\partial}x}\phantom{\rule{mediummathspace}{0ex}}\mathrm{d}x$

I think that it comes from considering the classical momentum:

$\u27e8p\u27e9=m\frac{\mathrm{d}\u27e8x\u27e9}{\mathrm{d}t}$

and that the expected value of the position is given by:

$\u27e8x\u27e9={\int}_{-\mathrm{\infty}}^{\mathrm{\infty}}x\phantom{\rule{mediummathspace}{0ex}}{|\psi (x,t)|}^{2}\phantom{\rule{mediummathspace}{0ex}}\mathrm{d}x$

But when replacing $\u27e8x\u27e9$ and differentiating inside the integral I don't know how to handle the derivatives of $\psi $ for getting the average momentum formula. Any suggestion?

Researching through the expected value formula probability examples, make sure that you focus on the values, variables, and the equations that make up the formula. Basically, your work should start at: E ( X ) = μ = ∑ x P ( x ). There are questions that may be exactly like what you need to solve, which is why you should take a look at the answers and see how the probability factor has been used. It will also help high school students to find the answers when you need an expected value formula calculator or want to find a quick push to your solution.