Value Definition and 1000 Threads

See my image for my attempt at solving this problem. My approach varies significantly from the solution I have for this problem and I wanted to get feedback on if what I did is correct of where I went wrong. thanks.

Hello everyone. If X, Y are two independent geometric random variables of parameter p, and Z=X+Y, what's E[X|Z=z]? I have calculated the distribution of P(Z=z) and I have then found that the conditional probability P(X=x|Z=z) equals 1/(z-1). How can I now find the conditioned expected value?

Refreshing on this...This is a relatively new area to me ...my solutions should be correct...what i am trying to engage on is if there are any other ways of looking at the same problem. Ok in my working i have, ##30 + 35 \cos β-45=0## ##\cos β=0.4286## ##β = 64.62^0, ⇒θ=25.4^0 ## to one...

How would we define a value for acceleration if only the direction is changing and not the speed?

Q： Why the entropy value of this steady flow open system is not equal to zero? My idea is as represented by the following equation. $$ \frac{dS_{sys}}{dt}=0,\,\,\,\,dt\ne 0 $$ $$ \therefore dS_{sys}=0\,\,\,\,\,\,\,\,\therefore ∆Ssys=∆Sair=0 $$ $$ \therefore...

The question was this: My calculations show that the answer should be equal to work done on crate to make it reach the same velocity which is equal to 216 J but the answer given is 432 J It is believed that extra energy is needed to overcome friction but friction is an internal force and...

hi all how do I prove that $$ <A^{n}>=<A>^{n} $$ It seems intuitive but how do I rigorously prove it, My attempt was like , the LHS can be written as: $$ \bra{\Psi}\hat{A}.\hat{A}.\hat{A}...\ket{\Psi}=\lambda^{n} \bra{\Psi}\ket{\Psi}=\lambda^{n}\delta_{ii}=\lambda^{n} $$ and the RHS equal: $$...

For this problem, Why cannot we say that ##f(2.999999999) ≥ f(x)## and therefore absolute max at f(2.99999999999999) (without reasoning from the extreme value theorem)? Many thanks!

For this, I don't understand how they solved, Because we would have to take the inverse of both side which would give the inverse of the matrix ##2 \times 2## matrix on the left hand side which dose not have an inverse. Dose anybody please know how they did this? Many thanks!

First lets focus on ##|x|## which is defined as distance between ##x##and ##0##. But if we look into it closely $$13=|-11-2|$$ which is distance between -11 and 2 but $$13=|11-(-2)|$$ which means this is distance between 11 and -2. Which is it? In the same way $$x=|x-0|$$ is distance between 0...

This is taken from Cranes Technical paper 410M problem 7-12. I cant seem to get the Korifice value by substituing the Cd and beta value. For example for beta = 0.7 & C = 0.7, I'm calculating Cd = 0.61 and Korifice = 28.0 (not 4.34 as shown) using excel. Is this an error?

There is some discussion currently and I was hoping to get some opinions here. The question is in regard to a Hook's law problem. The text gives the problem as seen below. The text says the answer is 50lb/in. Several people have tried from several different approaches. Factoring the "y" equation...

For this (ii), The solution is ##\lambda = \frac{4}{3}##, however when I tried solving the problem I did not get their answer. Dose somebody please guide me to their solution and tell me what I did wrong with my method below: ##\textbf {PR} = -3\hat i + 6\hat j - 2\hat k## ##\textbf {RS} =...

Looking at integration today...i will go slow as i also try finish other errands anyway; i am thinking along these lines; $$\int \sqrt{(ax^2+bx+c)} dx=\sqrt{a}\int \sqrt{\left[x+\frac{b}{2a}\right]^2+\left[\frac{4ac-b^2}{4a^2}\right]} dx$$ ... Therefore, $$\int_0^2 \sqrt{(8t^2+16t+16)}...

Dose someone please know why they have the absolute value bars in this derivation? many thanks!

Will the probability to provide a negative value of a Sz 1/2 spin system always be 0? If lambda 1 = hbar/2 and lambda 2 = -h bar/2 ?

I recently conducted a physics lab to measure the surface resistivity of a conductive sheet of a paper with a carbon filler. The theoretical Rs is approx. 5,000 Ω/☐ for this paper and yet we have calculated two Rs values: Rs when Varying Length and holding Width = 10100 +/- 83.07 Ω/☐ Rs when...

Is it possible for a limit of a range of functions to return a function? Example: f(z)= limit (as p approaches 0) (xp-1)/p.

Hello friends. How can I find the stopping power for a single energy value in the fluka? Which card should I add to the input file for this?

I am trying to find the expected value of the variance of energy in coherent states. But since the lowering and raising operators are non-hermitian and non-commutative, I am not sure if I am doing it right. I'm pretty sure my <H>2 calculation is right, but I'm not sure about <H2> calculation...

##\begin{align} \langle E \rangle &= \int_{\mathbb R^3} \int_{\mathbb R^3} \int_{\mathbb R^3} \int_{\mathbb R^3} g^\dagger (\tilde K) g(K) |\psi_0(x)|^2 \left(E_0 +\frac{\hbar^2 |K|^2}{2m}\right) e^{i(K-\tilde K)\cdot X -\frac{i}{\hbar} \left(\frac{\hbar^2 |K|^2}{2m}-\frac{\hbar^2...

Hi, I had to calculate the entropy in a task of a lattice gas and derive a formula for the pressure from it and got the following $$P=\frac{k_b T}{a_0}\Bigl[ \ln(\frac{L}{a_0}-N(n-1)-\ln(\frac{L}{a_0}-nN) \Bigr]$$ But now I am supposed to calculate the following limit $$\lim\limits_{a_0...

Im a having trouble understanding how this exactly works. $$ |x^2 - 4| < |x^2+2| $$ So I know the usual thing to do when you have absolute values,here it is even simpler since the right part of the inequality is always positive so I just have these 2 cases. 1. ## x^2-4 >= 0 ## and 2. ## x^2-4...

My interest is on part (e) only parts a - d were quite easy. I seek an alternative approach for part (e) ...phew this was a nice one ...took me time to figure out. :cool: Find the text solution here: My take/approach; We have ##a=0.6 m/s^2##, therefore; using ##s=ut+\dfrac{1}{2}at^2##, we...

Hi, First of all, sorry if this is not the right place to post my question I was not sure where exactly to post this kind of question. I'm wondering how can I find the value of a constant experimentally. For instance, I have a equation ##l = AB^{4/3}##, with a set of data for ##I## and ##B##...

For this problem, The solution is, However, why did they assume that the electric field produced by charge q is always pointing to the left at the origin? Many thanks!

I got to the quadratic equation of the motion where: 4gt^(2) - g(delta t)t - g(delta t) = 0 and tried to solve for t. In this case, we would take the positive discriminate since we are dealing with the passing of time. t = ((sqrt(17) g(delta t)) + g (delta t)) / (8g) However, this is the...

Hi, I have a Python 3 algorithm to output the "Runner Up", not originally mine: We're given a list of numbers and we're expected to output the second largest of these. It runs well, but I'm unclear as to what output is/are expected n=int(input()) arr=map(int,input().split())...

3 A+ 2 A = 7 A+ I I = -2A How the current can be in negative direction? If the sign if negative, doesn't it mean that the current will move towards the point P? Also If I am taking the 2A to be positive then Kirchhoff's law isn't satisfied as 5A≠7A

The first thing I did is to get the value of ##N_A## by the equaiton of ##\sum{}^{} M_B=0 \rightarrow 650*0.4+450*0.45+400=N_A*0.6 \rightarrow N_A = 104.2N## This is the first. The magnitude of the reaction at B: ##\sum{}^{} F_y=0 \rightarrow B_y=450+650,\sum{}^{} F_x=0 \rightarrow...

Here is Lars Olsen's proof. I'm having difficulty in understanding why ##y## will lie between ##f_a (a)## and ##f_a(b)##. Initially, we assumed that ##f'(a) \lt y \lt f'(b)##, but ##f_a(b)## doesn't equal to ##f'(b)##.

The Eddington Experiment famously confirmed GR by showing, as Einstein had predicted, a deflection of starlight by the Sun that was double the deflection expected by Newtonian gravity. I don't understand where Einstein's 2x number came from. I make the following assumptions: 1. That a ray of...

I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.

When specifying DC vs AC voltage excitation, is it appropriate to type 50 VDC with DC as a subscript? OR should it be "V DC"? The same concept if it were AC.

Hi PF Searching on the Internet, I've found this definition: Definition: Euler's Number as a Limit (i) ##e=\displaystyle\lim_{x\to{0}}{(1+x)^{\displaystyle\frac{1}{x}}}## and (ii) ##e=\displaystyle\lim_{n\to{\infty}}{(1+\displaystyle\frac{1}{n})^n}## Questions: 1-Does it make sense...

it is known that azimutal quantum number takes the values from 0 to n-1. how did they find it ?

What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...

We have to prove: If ##f: [a,b] \to \mathcal{R}## is continuous, and there is a ##L## such that ##f(a) \lt L \lt f(b)## (or the other way round), then there exists some ##c \in [a,b]## such that ##f(c) = L##. Proof: Let ##S = \{ x: f(x) \lt L\}##. As ##S## is a set of real numbers and...

I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.

Can't figure out the code below why the second output in main outputs 101 instead of 1. Something about calling ob1.reverse(s) before the pointer points to reverse(s), but I'm confused. Any help is much appreciated. #include <iostream> class Solution { private: int r = 0; int new_num =...

Apart from the usual integral method, are there any other ways to find expectation value of momentum? I know one way is by using ehrenfest theorem, relating it time derivative of expectation value of position operator. Even using the uncertainty principle, we might get it if we know the...

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so from Fourier transform we know that Ψ(r)=1/2πℏ∫φ(p)exp(ipr/ℏ)dp I proved that <p>= ∫φ(p)*pφ(p)dp from <p>=∫Ψ(r)*pΨ(r)dr so will the same hold any operator??

If X and Y are independent standard Gaussian variables, find the expected value of the maximum of X and Y. Note: This problem is due to @Office_Shredder.

When the expectation value of spin in the z direction for one particle is zero and I make measurements for an even number of particles in the same state, do I get exactly half to be spin up and half to be spin down along the z direction? More generally, what does spin expectation value for one...

Indeterminate forms are: ##\frac{0}{0}, \frac{\infty}{\infty} , \infty - \infty, 0 . \infty , 1^{\infty}, 0^{0}, \infty^{0}## My answer: 4, 9, 15, 17, 20 are inderterminate forms 1. always has a fixed finite value, which is zero 2. ##0^{-\infty}=\frac{1}{0^{\infty}}=\frac{1}{0}=\infty## so it...

First off sorry if something doesn't make sense, english is not my native language. I know i should start with sin2 α + cos2 = 1, but ant really continue from it. i am being confused by cos α = √5/3 since i know it isn't found in normal trig tables. So my problem is how to find out values of...

What is a "transient" value, result, or state in the Ising model? How do we treat these values during the simulation? Do we discard these values? If so, why?

So I ran a python simulation of 1,000 games of toss (50/50 odds) where each game consists of 100,000 consecutive flips. The result was this: 1000 is our starting balance and as expected, there's a nice normal distribution around it. I also calculated the average value after all the games and it...

I'm not asking it from "will it be secure" point of view, rather I'm asking textbook kind technically correct or not. This is the algorithm (in the 3rd step of right figure, it should be generate y, typo) I took p=23,g=5. And picked x=4,y=5 I got the secret key as 12 and both got 12, so it...