Variables Definition and 1000 Threads

Hello Forum, When the force ##F## and its resulting acceleration ##a## have the most general form, the acceleration can depend on the position ##x##, time ##t## and speed ##v##. Newton's second law is given by ## \frac {d^2x}{d^2t}= a(x,t,v)##. When the acceleration is only a function of...

Calculation of probability with arithmetic mean of random variables There are 4 people, each of whom has one deck of cards with 500 cards that are numbered from 1 to 500 with no duplicates. Each person draws a card from his deck and I would like to calculate the probability of the event that...

Homework Statement Let D be the triangle with vertices (0,0), (1,0) and (0,1). Evaluate: ∫∫exp((y-x)/(y+x))dxdy for D by making the substitutions u=y-x and v=y+x Homework EquationsThe Attempt at a Solution So first I found an equation for y and x respectively: y=(u+v)/2 and x=(v-u)/2 Then...

I have been studying multivariable calculus but I can't quite think visually how a function will be differentiable at a point. How can a function be differentiable if its partial derivatives are not continuous?

Hey. I am planning on doing some research, where I predict a change based on different types of risk. The question is simple. Can I use values of standard deviation as independent variables in a linear regression analysis (OLS)? The standard deviation values over time will be calculated in...

Hello all It's been a while ,as I read the almost daily news on climate change , some question come up to my mind , dose the ionosphere has any effect on climate change , as we all know now the Earth magnetic field is weakening ,and the temperature is rising ,dose this two variables related to...

Homework Statement Determine if the following function is continuous: f(x) = (x-iy)/(x-1) Homework Equations How do find out if a function is continuous without graphing it and without a point to examine? I know I've learned this, probably in pre-calculus too, but I'm blanking The Attempt at...

1. Homework Statement I want to calculate the rotational period and surface velocity of a Bishop Ring with a radius of 80 km and a surface 'gravity' of 0.86 G I should note that this isn't for homework. It's for personal interest. I'm looking for a sanity check on this. The homework forum...

Homework Statement Is the least count constant for Vernier scale like 0.1 mm or variables? 2. The attempt at a solution If the main scale readings are 10 mm and the vernier scale readings are 9 mm, the least count is MSD/VSD = 9/10 = 0.9 So the least count is 0.1 mm for every count in the...

Homework Statement Suppose that the number of eggs laid by a certain insect has a Poisson distribution with mean ##\lambda##. The probability that anyone egg hatches is ##p##. Assume that the eggs hatch independently of one another. Find the expected value of ##Y##, the total number of eggs...

I want to find the probability density function (pdf) of the difference of two RV's, p_{\Delta Y} = p_{(Y_1 - Y_2)},where y = \sin \theta, and where \theta_1 and \theta_2 are random variables with the same uniform distribution p_{\theta}=\mathrm{rect}\left(\frac{\theta}{\pi}\right). This has...

Hi all, I have a few questions regarding the issue of independence. Many thanks in advance. ##\textbf{1}## If I find that some events ##A, B, C## obey the following formula $$P(A \cap B \cap C ) = P(A)P(B)P(C)$$ it does not necessarily mean that a) they are mutually independent and b) ##A##...

A single particle Hamitonian ##H=\frac{m\dot{x}^{2}}{2}+\frac{m\dot{y}^{2}}{2}+\frac{x^{2}+y^{2}}{2}## can be expressed as: ##H=\frac{p_{x}^{2}}{2m}+\frac{p_{y}^{2}}{2m}+\frac{x^{2}+y^{2}}{2}## or even: ##H=\frac{p_{x}^{2}}{2m}+\frac{p_{y}^{2}}{2m}+\frac{\dot{p_{x}}^{2}+\dot{p_{x}}^{2}}{4}##...

Homework Statement If the random variables T and U have the same joint probability function at the following five pairs of outcomes: (0, 0), (0, 2), (-1, 0), (1, 1), and (-1, 2). What is the covariance of T and U? Homework Equations σxy = E(XY) - μx⋅μy The Attempt at a Solution My issue with...

Can you figure out what the answer of (x-a)(x-b)(x-c)...(x-z) is? This problem seems very tricky and you might think you need to expand one by one, but if you think carefully, you will find out that the answer is very simple! Solution:

Hello, I am a rising sophomore in Astronomy and Physics. I am taking complex variables next semester and was wondering the effort required to succeed in the class. There are some other classes I'd like to take, however I don't want to overload myself. I have taken up through multivariable calc...

A common use of the Fourier transform in physics is to transform between momentum-space and position-space. But what physical variables am I allowed to transform between? For instance can I use the Fourier transform to go from momentum space to frequency space or whatever?

2000 $\textsf{solve the given differential equation}$ $$y'=\frac{x^2}{y}$$ ok this is a new section on separable equations so i barely know anything but wanted to post the first problem hoping to understand what the book said. thanks ahead...

Hello (I'm reposting this from stack exchange, and thought this site may be more appropriate, so if you see it that's why), I'm working through this paper, and have encountered "a little algebra shows that...", yet I'm not familiar enough with the topic at hand to figure this out. Here is the...

Homework Statement I am trying to understand the very last equality for (let me replace the tilda with a hat ) ##\hat{P_{X}(K)}=\hat{P(k_1=k_2=...=k_{N}=k)}##(1) Homework Equations I also thought that the following imaginary exponential delta identity may be useful, due to the equality of...

hello everyone, recently i was studying thermodynamics and i think i got a basic doubt on what my book has to say and although i feel this is a small thing to ask but since i have no teacher with me, this is the best place i can think of. so my book was saying about intensive and extensive...

I don't think this is related to linear dependence/independence of linear algebra. I am talking about multi-variable calculus. I am getting confused with being able to quickly tell which variables depend on others when there are 4+ variables involved. For example, suppose I have w(r,s)...

I was just reading this paper: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.130401 It essentially shows that if the dynamics of the signalling mechanism in a nonlocal hidden variable theory were computable, then Alice and Bob in the typical EPR set up could use it to signal to...

Show that The standard deviation is zero if and only if X is a constant function,that is ,X(s) = k for every s belonging to S,or ,simply X=k. When they say constant function it means every element in S is been mapped to single element in the range.That is the single element is k. Which means...

Here is the problem statement in my book Here is the solution as per my book I don't understand that marked part. Is that correct? Can we write that? How? Need help to understand that part.

Homework Statement [/B] Homework Equations $$f_u- \frac{d}{dx} \left(f_{u'} \right) = 0 $$ $$f_v- \frac{d}{dx} \left(f_{v'} \right) = 0 $$ The Attempt at a Solution So I calculated the following, if someone could check what I've done it would be greatly appreciated, but I'm not convinced...

Homework Statement Find the cosine of the angle determined by the intersecting lines m1: (x,y,z) = (-2,1,4)+s(1,-3,4) m2: (x,y,z) = (-2,1,4)+t(-2,3,2) s and t are free variables Homework Equations a⋅b = length(a)length(b) cosθ The Attempt at a Solution I just did this equation using no...

Hi, Lets say I have N independent, not necessarily identical, random variable. I define a new random variable as $$Y=Σ^{N}_{i=0} X_{i}$$ does Y follow a normalized probability distribution?

Homework Statement In a given society, 15% of people have the sickness "Sa" , from them 20% have the sickness "Sb". And from those that don't have the sickness "Sa", 5% have the sickness "Sb" 1-We randomly choose a person. and we define: A:"the person having Sa" B:"the person having Sb"...

I am not sure how I should set my u and v expressions into the u-v plane for this question. How should I look at the expression to set u and v expressions?

I have obtained as such using changing of variables/ transformations: Let u= y/x and v= xy after manipulating the equation of the curves as such xy = 5, xy = 2, y/x = 1 and y/x = 4. Then u = 1, u = 4, v = 5 and v = 2 => obtain a square on the u-v plane. Change the integrand to: Outer...

Homework Statement Let ##X_1 \sim N(3,2^2)## and ##X_2 \sim N(-8,5^2)## be independent. Let ##U=aX_1+bX_2##. What is the distribution of ##U## Homework EquationsThe Attempt at a Solution As they are independent, we can write the distribution of ##U## as the convolution of the 2. So I get...

I have a pair of correlated datasets that I collected in the lab for temperature and conductivity of a solution vs time. I want to determine the functional relation between the two. (see attached plot-an interesting lead/lag in the phase difference). If I were trying to determine this...

Homework Statement I have never formally studied complex analysis, but I am reading this paper: http://adsabs.harvard.edu/abs/1996MNRAS.283..837S wherein section 2.2 they make use of the residue theorem. I am trying to follow along with this (and have looked up contour integration, cauchy's...

Hi, I have this random variable ##\beta=\sum_{k=1}^K\alpha_k##, where ##\{\alpha_k\}_{k=1}^{K}## are i.i.d. random variables with CDF ##F_{\alpha}(\alpha)=1-\frac{1}{\alpha+1}## and PDF ##\frac{1}{(1+\alpha)^2}##. I want to find the CDF of the random variable ##\beta##. So, I used the Moment...

Homework Statement A scalar is given by It is controlled by With step time h = 0.2 s 1. Find the discrete equivalent model 2. Check the stability of closed loop (K = +1) 3. Obtain the via the Bode plot Homework EquationsThe Attempt at a Solution So for question 1. This is where I'm...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $\mathbb{R}^n$" I need some help with an aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n" I need some help with an aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows: At the top of the above...

Hi, I have empirical data from my experiments. There are 2 columns of data (2 interdependent variables- temperature and viscosity).. 1 column (temperature) is input variable (temp. of tested material, once it was melted, it was gradually increased during the experiment). 1 column (viscosity)...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's Example 3 on pages 65-66 ... Kantorovitz's Example 3 on pages 65-66 reads as follows...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's Example 3 on pages 65-66 ... Kantorovitz's Example 3 on pages 65-66 reads as follows: In the above example, we read...

(I) Find the limit (x,y)->(0,0) of F, then prove it by definition. (II) Find the limit and prove it by definition of: as (x,y) approach (C,0), C different from zero. I have previously asked it on Quora, but it doesn't appear to have answers any...

Homework Statement ## x^2 +xy + y^2 = 3## ## y^2+yz+z^2=1## ##z^2+zx+x^2=4##Homework EquationsThe Attempt at a Solution ##yz^2-xz^2+yx^2-xy^2=4y-x## ##z^2(y-x)-xy(y-x)=4(y-x)## thus ##z^2-xy=4## or ##z^2=4+xy## ......on working out i end up with ## z^4-8z+16+(z^2-4)y^2+y^4= 3y^2## and ##...

Homework Statement The same potato chip company reports that their bags of family sized chips each follows an approx. Normal distribution with a mean of 10.72 ounces and a standard deviation of 0.2 ounces. If the company wants to ship these chips into boxes that contain 6 bags, what would be...

Homework Statement [/b] This is mentioned in my maths book, I m not able to understand it what they did. Homework EquationsThe Attempt at a Solution

Hi All, Is there a technique other than PCA (Principal Component Analysis) to decide whether it is somehow reasonable to group together , aka " collapse" several non-continuous ( Categorical, Likert, Ordinal, etc. ) into a single one. The idea is, of course, to lose only a negligible amount of...

##f(x,y)## a critical point is given by ##f_x=0## and ##f_y=0## simultaneously. the test is: ##D=f_{xx}f_{yy}-(f_{xy})^2 ## if ##D >0 ## and ##f_{xx} <0 ## it is a max if ##D >0 ## and ##f_{xx} >0 ## it is a min ##D >0 ## is is a saddle if ##D =0 ## it is inconclusive, and ##f_x## and...

I'm doing a research project over the summer, and need some help understanding how to construct an inverse Fourier transform (I have v. little prior experience with them). 1. Homework Statement I know the explicit form of ##q(x)##, where $$ q(x) = \frac{M}{2 \pi} \int _{- \infty}^{\infty} dz...

My question is about basic algebra. I am thinking about the "why" here and I'm looking for an intuitive answer.If you have the following equations: =>S+U=90 =>S+U=90 and =>40S+25U=2625 =>40S+25U=2625 you can then rewrite S=90−U and then substitute. Now you have a single equation with one...

Hi PF! Regarding matched asymptotic expansions, given an ODE BVP, I have learned a boundary layer can arise, where we need to stretch the independent variable through carefully selection i.e. if ##x## is the independent variable, perhaps ##\phi = (1-x)/\epsilon : \epsilon \ll 1##. Would we...