Distribution Definition and 1000 Threads

a) Let X = distance walked on Friday and Y = distance walked on Saturday X ~ N (12, 0.192) and Y ~ N (10, 0.52) Let A = Y - X → A ~ N (-2 , 0.2861) P(Y > X) = P(Y - X > 0) = P(A > 0) = 9.2 x 10-5 But the answer key is 0.026 Where is my mistake? Thanks

Hi, I was attempting this problem from the MIT OCW website probability and statistics course. Context: When Jane started class, she warned Jon that she tends to run late. Not just late, but uniformly late. That is, Jane will be late to a random class by ##X## hours, uniformly distributed over...

Is it correct to say that $$\int e^{-i(k+k’)x}\,\mathrm{d}x$$ is proportional to ##\delta(k+k’)##?

I am not really sure what the reason is but my argument would be if normal distribution is appropriate, then almost all the score will fall in the range of μ - 3σ to μ + 3σ For this case, the range of μ - 3σ to μ + 3σ is 26.6 to 118.4 and all the score is unlikely to be within the range. I...

Hi, I was recently reading through Systems Kinetic Modeling notes and am struggling to understand the concepts of total volume of distribution and total body clearance. As far as I understand, the total volume of distribution ## V_c ## is the "volume of the compartment into which the...

Circuit runs from q0 to q1, some E field (our charge source/sink) 1. Is the current running from q0 to q1 impacted by the existence of the B field? For example, if there were no B field, current would flow from q0 to q1, let's call it I0. When we flip on the B field what effect is there on the...

1. The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight...

Greetings! I started working through a book of statistical mechanics, and I struggle with properly deriving a formula that makes intuitive sense. I will describe the situation and then my own solution attempts. Suppose we have two systems ##j## and ##k## of volumes ##V_j## and ##V_k## and...

Hi, I was attempting the problem above and got stuck along the way. Problem: Suppose that ## Y_1 ## and ## Y_2 ## are random variables with joint pdf: f_{y_1, y_2} (y_1, y_2) = 8y_1 y_2 for ## 0 < y_1 < y_2 < 1 ## and 0 otherwise. Let ## U_1 = Y_1/Y_2 ##. Find the probability distribution ##...

Hello! Assume I have a classical system at a fixed temperature, such that the energy can be described by a Boltzmann distribution at that temperature. If I have a huge number of such systems in that state, and I measure the energy of each one, independently, the probability of measuring a given...

Let us suppose we are given a Gaussian Distribution in the form of $$p(x,y) \propto exp(-\frac{1}{2}x^2 - \frac{1}{2}by^2 - cxy)$$ What are the equations that I need to use to obtain Mutual Information ?

The first step is to group the data and make a table so I can get the observed frequency for each data interval. I did two different groupings (something like 150 - 160 , 160 - 170 , etc and the other is 150 - 170, 170 - 190, etc) and found out that the conclusion of the hypothesis is different...

SA I study the reflection from a rough surface and get the field as the attached figure my question can I use the field distribution to get the angular distribution of the scattered field and how can I project the field to plane waves?

I think the idea is to first count the number of ways the questions are passed out without restrictions and then subtract the number of ways the two easy questions are together. Call each student ##s_1,s_2,s_3##. We know their total number of questions is 8, so ##s_1+s_2+s_3 = 8 : s_1,s_2,s_3 >...

My attempt : $$P(n) = \frac{1}{\mathcal{Z}} Exp[(n\mu -E)/\tau]$$, use $$\lambda = e^{\mu/\tau}$$, then the distribution can be written as $$P(n) = \frac{1}{\mathcal{Z}} \lambda^nExp[-E/\tau]$$ Note that the average number of particle can be written as $$<N>= \lambda \partial \lambda ( log...

I know for muons that the the probability that a muon decays in some small time interval ##dt## is ##\lambda dt##, where ##\lambda## is a decay rate. Thus the change in the population of muons is just ##dN/N(t) = −\lambda dt##. Integrating gives ##N(t) = N_0 \exp(−\lambda t)##. This makes sense...

What is a "temperature distribution" in the context of a stellar photosphere and How is the temperature distribution related to the effective temperature?

Hi hi, I was thinking about this, all of this starts playing a game, I'll show a simplification: We ca win several times. We have a count ##n##, where is the max number of rolls until you win, let's say we can win a ##m## amount. In every roll we can win ##m## with a probability of ##p##. If...

Hello everybody at the forum I'm from Ukraine, I have Chemistry degree, and last year I began to self studying Quantum Mechanics. I'm reading this article: R. Garcia, A. Zozulya, and J. Stickney, “MATLAB codes for teaching quantum physics: Part 1,” [Online]. Available...

Hello, I was wondering if someone could show me how to determine the number of orbitals available for a state and the number of electrons in that state. For calcium in the ground state, the electron config is 1s2 2s2 2p6 3s2 3p6 4s2. For the first excited state I assumed 1s2... 4s1 3d1. From...

Hey! :giggle: Let $X$, $Y$ and $Z$ be independent random variables. Let $X$ be Bernoulli distributed on $\{0,1\}$ with success parameter $p_0$ and let $Y$ be Poisson distributed with parameter $\lambda$ and let $Z$ be Poisson distributed with parameter $\mu$. (a) Calculate the distribution...

Summary:: I have been provided with the table in which N and occurence are given. I have been asked to calculate the 1. Total count 2. mean count 3. mean count. Now, assuming our distribution described by Poisson's we need to calculate the tasks. The Poisson's distribution is given by...

This source http://sustainableaviation.org/sas2017/session/prandtl-wing-maximum-efficiency/index.html claims : "Bell lift distribution can be applied to propulsion systems (no more “minimum induced loss”). We believe this results in a gain of 15.4% thrust for the same input torque/power." Bell...

What is ideal lift distribution for propeller blade to get best thrust/power ratio? To do this blade must has minimum drag, because drag releted to torque,and torque x RPM= power..

If the high energy ion spectra is similar to that of Maxwell-Boltzmann distribution, possible to consider it as High Energy Maxwell-Boltzmann distribution? The ion spectrum is obtained due to the electric discharge in gas; and the peak energy is 30 keV and end point energy is 1.5 MeV and it is...

Hi With the exact Boltzmann distribution, ni = InverseDigamma(-α-β*εi)-1: https://studyres.com/doc/269738/revision-of-boltzmann-statistics-for-a-finite-number-of-p... Shouldn't I be able to get (n0, n1, n2, n3, n4, n5, n6, n7) = (6, 3, 2, 0, 0, 0, 0, 0) for some α and β, if N=11, E=7 and Δε=1...

How do I simplify the expression...

Hi, I have question about finding marginal distributions from 2d marginal pdfs that lead to the probabilities being greater than 1. Question: If we have the joint probability distribution ## f(x, y) = k \text{ for} |x| \leq 0.5 , |y| \leq 0.5 ## and 0 otherwise. I have tried to define a square...

From an excel file I can get the probability of each energy state Εi and I saw at Wikipedia that the probability of each energy is proportional with e^−Εi/KT, from this I find the energy of every micro state. Also from the formula which I found on a paper I can get a curve like the curve...

If we take a spherical distribution of matter wherein gravitational force and cosmological-constant force are equal upon an object on its surface, then does the time that it took for that volume to grow to the size wherein the two forces are equal match the time it took for the universe to start...

Looking for good sources, something beyond typical popular science but readable for a layperson that details current thinking on how various elements get created and distributed over time (supernova, neutron star mergers etc) and implications for evolution of life. Any recommendations?

hi guys i was trying to solve this non linear ode using the shooting algorithm in Matlab : i am not sure how to solve it using the normal shooting algorithm i have , since no other boundary at x = L/2 was given to check the shooting ?! function dTdx = bar_temp(x,y) k = 72; h = 2000; epsilon =...

Variation coefficient is calculated by And the very definition of poisson distribution is that $$\mu = \sigma $$ So how would any other value but 1 be a possible?

A spherical volume charge (R<=1cm) with uniform density ρv0 is surrounded by a spherical surface charge ( R=2cm) with charge density 4 C/m2. If the electric field intensity at R=4cm is 5/Є0 ,deterime ρv0

this is a textbook problem shared on a whattsap group by a colleague... i have no problem in finding the value of ##k=0.08##, i have a problem with part (ii) of the problem. I have attached the solution here; how did they arrive at the probability distribution of ##y##? attached below is...

First of all, this is question from the modern physics module in 1st year physics program. The problem is I have no prior knowledge about spectroscopy or Lorentzian profile. However, the Compton scattering topic was already introduced. The Compton scattering formula can be changed into the...

I feel this is not correct, from my understanding of data, discrete data will always have a corresponding discrete frequency table and continuous data will always have a corresponding continuous frequency table. The class interval ought to be ##0≤x<5##, ## 5≤x<10##... i need clarity on this...

According to my professor, the solution in this book (pages 20-21) for item (ii) is wrong: https://www.u-cursos.cl/usuario/75468645ed16a71af6da3ffd813d47f5/mi_blog/r/Problems_and_Solutions_on_Electromagnetism.pdf

Hello, I have to find an expression for the total movement of a bacteria ##s##, knowing that the bacteria is placed (centered) on a two side ruler at position ##x=0## (so a negative ##x## value means the bacteria has moved to the left of the ruler) and that the probability it moves to ##x## is...

a) Static charge distribution should result in a static electric field? Legitimacy should be checked with curl of E = 0? b) Using the second equation should give is the answer?

For medium to large nuclei, common sense suggests that protons should not be uniformly distributed inside the nucleus. Assuming the protons inside the nucleus are mobile (but supposing that it doesn't make sense to consider the nucleus a "conductor", in which case all charge would reside on the...

I have an Energy harvesting expression something like the following $R = \tau B \log\Big(1 + \frac{E h^2}{\tau r^\alpha\sigma^2} \Big)$ $E = \tau(2^{R/\tau B}-1 )\frac{r^\alpha\sigma^2}{h^2}$ Let all constant terms as $a$ to simplify the expression into : $E = a\frac{1}{h^2}$ $E$ is a random...

I am reading a journal article from Balduzzi about shear stress recover on tapered beams. I can not get the exact constants he gets and I am stumped. Above is solving for differential piece of the beam. Equations 16-18 are the ones I am trying to calculate. I attached my work and the...

So, it's a long way to the solution, but I'm finding it difficult to find a starting point. I'm going to say that as a first step, I should find what the value of the stream function ##\psi## is, at the surface. In order to do this, I need to use the following equation: ##F=\phi+i\psi## If I...

Given \begin{equation} \begin{split} \int_{y-\epsilon}^{y+\epsilon} \delta^{(2)}(x-y) f(x) dx &= f^{(2)}(y) \end{split} \end{equation} where ##\epsilon > 0## Is the following also true as ##\epsilon \rightarrow 0## \begin{equation} \begin{split} \int_{y-\epsilon}^{y+\epsilon}...

If we have a spin measurement with P(up)=0.5 en P(down)=0.5, this is equivalent to tossing a coin P(heads)=0.5 and P(tails)=0.5. The probability of having five heads and five tails out of ten tosses is the binomial: ##\binom{10}{5}(0.5)^5(0.5)^5##. So the same would hold for the spin...

Hi, I have this question: If random variable T is uniformly distributed over [a, b] , what is its failure rate? Please help

Since the "non-uniform" hypothesis I got confused about how to solve this problem... in which way could I find its center of mass, if its mass is not distributed uniformly? Another question I have with regards to this static situation is: is the beam placed horizontally? If not, how could I know...

Hi everyone, I was having a conversation with my friend about the many worlds interpretation of quantum mechanics, and we couldn't figure out if many worlds implied every single last possible conceivable outcome, or if there were certain limitations that the system was confined to. For...

Hello everyone, I am new to this site so I hope this is the right place to ask this. I understand simulating electric field intensity using electrostatics because E=V/d makes sense to me. I do not understand how to consider e-field intensity using charge distribution. When is charge...