Value Definition and 1000 Threads

For the following distributions find $$E[2^X]$$ and $$E[2^{-X}]$$ if finite. In each case,clearly state for what values of the parameter the expectation is finite. (a) $$X\sim Geom(p)$$ (b) $$X\sim Pois(\lambda)$$ My attempt: Using LOTUS and $$E[X]=\sum_{k=0}^{\infty}kP(X=k)=\frac{1-p}{p}$$...

Publication News article It looks increasingly like something is wrong with the older electron-based results. The story of "with electrons you measure one thing, with muons another" doesn't work any more. Is that a good thing (there might be some conclusion what the radius is in the next years)...

For question 2.2: <Ψ0|p|Ψ0> = ∫Ψ0 -iħ d/dx(Ψ0) =M Using Integration by parts i get: M = -Ψ0 iħ d/dx(Ψ0) (assuming hilbert space) Implying the expectation values for momentum are zero , however i get all the expectation values are zero for x and momentum in both states which makes no sense :(

$\tiny{219\quad inverse function}$ Let $f(x)=(2x+1)^3$ and let g be the inverse of $f$. Given that $f(0)=1$, what is the value of $g'(1)?$ $(A)\, \dfrac{2}{27} \quad (B)\, \dfrac{1}{54} \quad (C)\, \dfrac{1}{27} \quad (D)\, \dfrac{1}{6} \quad (E)\, 6$ so rewrite at...

I tried to do like this: \frac{((76 - 15)^4 + 324)((76 - 3)^4 + 324)((76 + 9)^4 + 324)((76 + 21)^4 + 324)}{((76 - 21)^4 + 324)((76 - 9)^4 + 324)((76 + 3)^4 + 324)((76 + 15)^4 + 324)} Then stucked Thanks

There are meaningful ways to assign values to things like 1 - 1 + 1 + ... or 1 - 2 + 3 - 4 + ... In a similar spirit, is it possible to assign a value to the integral of a function like this: ##f(x)=x*sin(x)## or this one: ##g(x)=Re(x^{1+5i})## (Integrals from some value, say zero, up...

L=100mh=0.1H ω=10^3 rad/s -> f = 159Hz XL= ωL= 2πfL= 2π*159*0.1= 99.90 Ω Z parallel = [(XL∠90º)*R2] / [(XL∠90º)-R2]= 37.13∠-21.8º XC= 1/ωC= 1/(2 π f C) I don't see how I am supposed to get to C

So i had this problem and I want a rigourous solution. The answer should be : Tmin=(I/sigma)^(1/4) and Tmax=(sqrt(3I)/sigma)^1/4

I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25. How do I derive the given equations?

Problem (c) for Discrete Value Ring for a unit I am stuck in the middle of a proof. Here is the background information from Dummit and Foote Abstract Algebra 2nd ed.: Let $K$ be a field. A discrete valuation on $K$ on a function $\nu$: $K^{\times} \to \Bbb{Z}$ satisfying $\nu(a\cdot...

If for a field say ##f=xyz## ,it's value is defined at 10 points in the 3-D Cartesian co-ordinate system...now using these 10 values of f and the corresponding coordinates is it possible to find the value of f at any ##(x,y,z)## of choice??

I need to decide if I want to continue onto a PhD in Electrical Engineering or exit with my MS. I'm not sure what to do, I think academics is kind of cool and I would like to learn more, on the otherhand I sort of want to start working on Real World projects that have some impact and making an...

I hope I am posting this in correct forum section. I just downloaded LTspice for my Power Electronics course. Does anyone know if the software can display the DC component of a waveform such as found by determining the Fourier series of a waveform?

$\tiny{31.6}$ Solve the initial value problem $Y'=\left|\begin{array}{rr}2 & 1 \\-1 & 2 \end{array}\right|Y +\left|\begin{array}{rr}e^x \\0 \end{array}\right|, \quad Y(0)=\left|\begin{array}{rr} 1 \\1 \end{array}\right| $ ok so we have the form $y'=AY+G$ rewrite as $$\displaystyle...

Hello guys, is it possible to "see" the mean value theorem when one is only thinking of numerical values without visualizing a graph? Perhaps through a real world problem?

How do I work out what m value (0, 1/2, 1 etc) to put in the thin film interference equations like 2nt = (m + 1/2)*lambda? Does it depend if it's constructive or destructive? Could someone help explain, thanks!

Would using mercury to form amalgam alloys combining gold, copper, and silver have any electronic value? Has this amalgam ever been made and tested in conductivity and Malleability? Or would it just be an expensive filling?

Reading The Theoretical Minimum by Susskind and Friedman. They state the following... $$\left|X\right|=\sqrt {\langle X|X \rangle}\\ \left|Y\right|=\sqrt {\langle Y|Y \rangle}\\ \left|X+Y\right|=\sqrt {\left({\left<X\right|+\left<Y\right|}\right)\left({\left|X\right>+\left|Y\right>}\right)}$$...

Hello, The relationship between entropy ##S##, the total number of particles ##N##, the total energy ##U(β)##, the partition function ##Z(β## and a yet to be defined constant ##β## is: $$S(\beta)=k_BN \cdot \ln(Z(\beta)) - \beta k_B \cdot U(\beta)$$ Which leads to: $$\frac{dS}{d\beta} =...

Just need a bit of guidance to make sure that I am heading the right way. Question is: Fig 3 shows the block diagram of the control of an electric heating system. The heater is driven from a voltage-controlled power supply, the voltage V1 being derived from a potientiometer. The output...

Hi, I'm working on a question now where I need to calculate the z value. which I have been able to but I'm calculating a value off the normal distribution that is on the left-hand side of the normal distribution curve and it needs to on the right side. As the value I'm looking into is higher...

##\delta(- N\mathcal{H}) = \delta(-N[\gamma^{-\frac{1}{2}}(Trπ ^2 - \frac{1}{2}(Trπ )^2 -\gamma^{\frac{1}{2}}R])## and I am going to concentrate on the first part and find ##\delta(-N[\gamma^{-\frac{1}{2}}(Trπ ^2 - \frac{1}{2}(Trπ )^2]) ## wrt ##g_{ij}##. ##\delta(-N[\gamma^{-\frac{1}{2}}(Trπ...

The result of h from my calculations is equal to about 162321138 when it should be about 400km or 400000m and I don't why.

find the solution of the given initial value problem: $6y''-5y'+y=0\quad y(0)=4 \quad y'(0)=0$ if $r=e^{5t}$ then $\displaystyle 6y''-5y'+y=(r-3)(r-2)=0$ then $y=c_1e^{3t}+c_1e^{2t}=0$ for $y(0)=4$ $y(0)=c_1e^{3(0)}+c_1e^{2(0)}=4$ ok I don't see how the last few steps lead to the...

I tried to find it the following way but to no avail: Let maximum value of ##\sigma## be ##S## Now unfortunately, we do not have a maximum value for ##\dfrac{1}{r^2}## because the field point can be as close as we want to the arbitrary surface charge. (The field at a point on the surface is...

Problem Statement: Prove that |a|=|-a| Relevant Equations: ##|a|= a, ## if ## a \geq 0 ## and -a, if ## a \leq 0 ## Somewhat stumped on where to start... i know that we need to use cases. If we consider ##a\geq 0##, then are we allowed to use the fact that ##|-a|=|-1|\cdot|a| = |a| ##? This...

In my earlier post, I demonstrated a way to derive MTW's Equation (21.90), ##16π\mathfrak{L}_{geom} = - \dot π^{ij} γ_{ij} - N\mathcal{H} -N_i\mathcal{H^i}-2(π^{ij}N_j-½N^iTrπ+γ^½N^{|i})_{,i}## MTW (21.90) I received my first two 'likes' for this which made me really happy - Thanks...

Find the value of $\theta$ if it exists $$\theta=\tan^{-1}\sqrt{3}$$ rewrite $$\tan(\theta)=\sqrt{3}$$ using $\displaystyle\tan\theta = \frac{\sin\theta}{\cos\theta}$ then if $\displaystyle\theta = \frac{\pi}{3}$ $$\displaystyle\frac{\sin\theta}{\cos\theta}...

##P^2=\begin{bmatrix} 1/2&0&1/2\\ 0&1/2&1/2\\ 1/2&1/2&0 \end{bmatrix} \begin{bmatrix} 1/2&0&1/2\\ 0&1/2&1/2\\ 1/2&1/2&0 \end{bmatrix}= \begin{bmatrix} 1/2 & 1/4 & 1/4\\ 1/4 & 1/2 & 1/4\\ 1/4 & 1/4 & 1/2 \end{bmatrix}## So, ##P(X_3 = 1|X_1 = 2) = 1/4##. Is this solution correct?

In the derivation of the Fermi-Dirac and Bose-Einstein distributions, we compute the Grand Partion Function ##Q##. With ##Q##, we can compute the espection value of the occupation number ##n_{l}##. This is the number of particles in the same energy level ##\varepsilon _{l}##. The book I am...

Hi everyone, initially let me introduce a concept widely used in ARIMA in the following. $$AICc = AIC + \frac {2k^2+2k} {n-k-1}$$ where n denotes the sample size and k denotes the number of parameters. Thus, AICc is essentially AIC with an extra penalty term for the number of parameters. Note...

Hello, Consider the system of linear homogeneous differential equations of first order dy/dx = A(x) y where x denotes the independent variable, A(x) is a square matrix, and y is an unknown vector-function...

From ##\vec r''(t)## we integrate to get $$\vec r'(t) = \left(-\sin(t)+C_1\right)\hat i + \left(6\cos(2t)+C_2\right)\hat j - \left(9.8t+C_3\right)\hat k$$ Solving for the C constants using ##\vec r'(0) = 1\hat i + 6\hat j + 0\hat k##, ##\vec r'(0) = <C_1, C_2, C_3>## ##=<1, 6, 0>## So we now...

My Textbook says this is the formula to find energy values for electron shells: $$E_{mol of electrons} = \frac{-1312kJ}{n^2}$$ where $n$ is in electron shell number But when we divide by 1 mol to get the energy value for each electron we get $$E_{electron} = \frac{-2.178 \cdot 10^{-18}}{n^2}...

Can it be treated like a rare commodity that is of high value? Gold isn't legal tender either but it's rarity and demand keeps the market value reasonably high. Are there any fundamental reasons why bitcoin wouldn't turn out to be like a precious metal? I'm talking long term. Right now, I...

Consider an integral of form $$\int_a^b dx f(x) g(x).$$ Is it possible to tell a numerical integrator to spit out the value of ##x \in [a,b]## that maximises the value of ##f(x)g(x)##? I'm mostly interested in incorporating this into some code I have for adaptive integrator gsl_qags in C++...

Let $m_n$ be the smallest value of the function: $$f_n(x)=\sum_{k=0}^{2n}x^k.$$ Show, that $m_n\to\frac{1}{2}$ as $n \to \infty$. Source: Nordic Math. Contest

Hi everyone, I am using a online y plus calculator to work out the y plus value for a fuel bundle. http://www.pointwise.com/yplus/ In regards to the reference length, I have been told by peers to utilise the hydraulic diameter using 4A/P where A is the cross sectional area, and P is the wetted...

Watching Dr. Susskind show how to find the time evolution of the average of an observable K, he writes: I can not for the life of me figure out he derived it, and he also did something which I found terribly annoying throughout which is set hbar to 1, so after steps you lose where the hbar...

I'm kind of confused on how to evaluate the principal value as it's a topic I've never seen in complex analysis and all the literature I've read so far only deals with the formal definition, not providing an example on how to calculate it properly. Therefore, I think just understanding at least...

Just interested in what may be achieved by putting a man/men on the moon again.

Hey, I've got this problem that I've been trying to crack for a while. I can't find any info for multi-variable expected values in my textbook, and I couldn't find a lot of stuff that made sense to me online. Here's the problem. Find $E(C)$ Find $Var(C)$ I tried to get the limits from the...

Homework Statement Hello today I am solving a problem where an electron is trapped in a potential well. I have a solved Schrodinger's Equation. I am having problems in figuring out what the wave function should be. When I solved the equation I got a complex exponential. I know I cannot use the...

Homework Statement Find the value of (-√3 + i)43/243 Homework EquationsThe Attempt at a Solution I do not know how to really go about this problem. I know that i0=1, i1=i, i2=-1, i3=-i, and I tried to use that to help but I got to no where, I also tried to break up the exponent into...

Homework Statement Solve the initial value problem y1'=-13y1+4y2 y2'=-24y1+7y2 y1(0)=5, y2(0)=2 Homework EquationsThe Attempt at a Solution Here is what I have: y'=[-13 4, -24 7]y I change it to A=[-13 4, -24 7] My eigenvalues are λ=-1 and λ=-5. My basis are [1/3 1] and [1/2 1]. Now I have...

Homework Statement I have a star that has an apparent magnitude of 13.73 with uncertainty of 0.03303 It's distance Modulus is 13.9967 so it's absolute magnitude is -0.26 The distance is 6300 parsecsHomework Equations [/B] The uncertainty on log10(d) is given by Δ(log10)≈0.4343 Δd/d ΔQ) =...

I don't know where to put this but it is a question which is bothering me. From the perspective of a physicist who wants to generate new theories, what's the value in spending significant time learning classical theories? People slave always at books like Jacksons Electrodynamics but it's not...

Homework Statement I have a value of $$ U=U_0+x (∂U/∂x)+y(∂U/∂y)+z (∂U/∂z)+1/2x^2(∂^2U/∂x^2)+1/2y^(2∂^2U/∂y^2)+...$$ We need to find the mean value of the U. So the answer is $$\overline{\rm U}\approx U_0+a^2/24(∇^2U)$$Homework Equations $$\overline{\rm U}=1/a^3 \int \int\int Udxdydz$$ The...

Moderator's note: This thread is an offshoot of https://www.physicsforums.com/threads/basic-cooking-physics.966819/ I cook all week long, need to chill home on weekends. I

\tiny{b.2.1.23} 1000 Solve the initial value problem and find the critical value $\displaystyle a_0$ exactly. $\displaystyle 3y'-2y=e^{-\pi/2}\quad y(0)=a$ divide by 3 $\displaystyle y'-\frac{2}{3}y=\frac{e^{-\pi/2}}{3}$ with integrating factor $\displaystyle e^{-2t/3}$ multiply through...