Continuous Definition and 1000 Threads

Homework Statement The random variable ##(x,y)## has density ##f(x,y) = ce^{-(ax+by)}## for ##0\leq y\leq x\leq 1##, with given constants ##a > 0##, ##b > 0##. 1. Compute the constant ##c##. 2. Find the conditional probability density ##f_y(y|x)##. 3. Compute the regression curve of ##Y## on...

Homework Statement Prove functions f and g are continuous in ℝ. It's known that: i) lim g(x)=1, when x approaches 0 ii)g(x-y)=g(x)g(y)+f(x)f(y) iii)f2(x)+g2(x)=1 The Attempt at a Solution [/B] g(0) has to be equal to 1 because it's known that lim g(x)=1, when x approaches 0. Otherwise g won't...

Homework Statement A continuous signal $$x(t)=15\sin (10t)+5\sin(30t)+3\sin(50t)$$ is sampled with frequency $\Omega =4.0$ Hz. Which frequencies are present in the sampled signal? Homework EquationsThe Attempt at a Solution No idea really. I seriously doubt it is that easy: Frequencies...

"If a function can be differentiated, it is a continuous function" By contraposition: "If a function is not continuous, it cannot be differentiated" Here comes the question: Is the following statement true? "If a function is not right(left) continuous in a certain point a, then the function...

Good day to you all, First, I want to let you all know that I'm new at this and that my question could be a bit vague so I'll try and do my best to explain what I want to know. I read on a forum about the Hubble's value decreasing over time despite the fact that the expansion of the Universe...

Suppose a certain function in continuous at c and (c. f(c)) exists, then which of the two could be false: \displaystyle \lim_{x \rightarrow c^-} {f(x)} = \lim_{x \rightarrow c^+} {f(x)}, and \displaystyle f'(c)? I feel like both could be false, because if the formal derivative at a point...

A continuous random variable x has the following probability function: f(X)=(X+1)/8 -1<=X<=3 0 Otherwise 1. Find the Pr(X<=2) 2. Find the mean of X

The motivation for this thread comes from physics, but I'm posting it in the maths section as the question is more of a mathematical one and less concerned with the underlying physics. In cosmology, they often talk about closed universes with positive curvature, or non-Euclidean elliptic...

I've just encountered this somewhere and I need some sort of formal proof for why a continuous function ##f(x)## can equal zero because its integral is zero. Are there any out there? I've seen similar forum posts on places like Stack Exchange and one here, but I can't exactly follow the logic...

Homework Statement Calculate the limit $$lim_{s,t→∞} R_X(s, s+t) = lim_{s,t→∞}E(X(s)X(s+t))$$ for a continuous time Markov chain $$(X(t) ; t ≥ 0)$$ with state space S and generator G given by $$S = (0, 1)$$ $$ G= \begin{pmatrix} -\alpha & \alpha \\ \beta & -\beta\...

This is probably stupid question but is it logically possible for a universe to exist where matter is continuous and not atomic? How would such matter be stopped from collapsing to a point?

Consider two functions f, g that take on values at t=0, t=1, t=2. Then the total error between them is: total error = mod(f(0)-g(0)) + mod(f(1)-g(1)) + mod(f(2)-g(2)) where mod is short for module. This seems reasonable enough. Now, consider the two functions to be continuous on [0,2]. What...

The following equation equates relativistic mass to rest mass http://scienceworld.wolfram.com/physics/RestMass.html Does the mass caused by high velocity have gravity?

So proofs are a weak point of mine. The hint is that a composite of a continuous function is continuous. I'm not really sure how to use that. What I was thinking was something to the effect of an epsilon delta proof, is that applicable? Something to the effect of: ##A \sim B\text{ and let } f...

Homework Statement Using the CTFS table of transforms and the CTFS properties, find the CTFS harmonic function of the signal 2*cos(100*pi(t - 0.005)) T = 1/50 Homework Equations To = fundamental period T = mTo cos(2*pi*k/To) ----F.S./mTo---- (1/2)(delta[k-m] + delta[k+m]) The Attempt at...

Most threads about making orbit changes assume impulsive changes in velocity (short period bursts). What if one wants to increase the radius of a circular orbit with a very small constant thrust? I assume the thrust should be applied tangentially in the direction of travel, but what would be the...

so I was reviewing my textbook on calculating electric field when we can assume a continuous charge distribution and they said three useful tools are (1) making use of symmetry (2) expressing the charge dq in terms of charge density lambda (3) and checking the answer at the limit of large r...

After reading some of the other posts on the Forum, I'm clear on the fact that Bohmian trajectories (of the de Broglie Bohm formulation) and the paths of the Feynman path integral formulation are very different things. I'm wondering (and it's a naive question, no doubt), when talking about...

Assuming that we have a chemical plant which produces methanol through the following equations: CH4 + H2O <--> CO + 3H2 CO + 2H2 <--> CH3OH CO2 + 3H2 <--> CH3OH + H2O I know that with specific pressure, temperature and flow rates, I can produce reactions with specific equilibrium constants. Are...

Homework Statement Suppose the distance X between a point target and a shot aimed at the point in a coin-operated target game is a continuous random variable with pdf f(x) = { k(1−x^2), −1≤x≤1 0, otherwise. (a) Find the value of k. (b) Find the cdf of X. (c) Compute P (−.5...

Homework Statement A nonconducting sphere 1.3 m in diameter with its center on the x axis at x = 4 m carries a uniform volume charge of density ρ = 4.8 µC/m3. Surrounding the sphere is a spherical shell with a diameter of 2.6 m and a uniform surface charge density σ = -1.2 µC/m2. Calculate the...

Homework Statement The length of satisfactory service (years) provided by a certain model of laptop computer is a random variable having the probability density f(x) = (1/4.5)e^(-x/4.5) for x > 0 and 0 for x <= 0 find the probabilities that one of these laptops will provide satisfactory...

My name is Bradley and I am a first year university student attending Intro to Quantum mechanics lectures but didn't understand... Why the black body radiation curve (unlike the quantized emission seen from atomic spectra), is continuous over all frequencies. I am wondering what exactly gives...

Homework Statement X ~ Uniform (0,1) Y = e-X Find FY (y) - or the CDF Find fY(y) - or the PDF Find E[Y] 2. Homework Equations E[Y] = E[e-X] = ∫0 , 1 e-xfx(x)dx FY(y) = P(Y < y) fY(y) = F'Y(y) The Attempt at a Solution FX(x) = { 0 for x<0 x for 0<x<1 1 for 1<x } fX(x) = { 1 for...

Homework Statement A disk with a radius of 0.6 m is given a uniform charge density of -7.2*10-9 C/m2. The disk is in the xz plane, and centered at the origin. A. What is the size and direction of the electric field at the point A, whose coordinates are (0m, 1.5m, 0m)? B. You now add an...

Title doesn't let me be sufficiently clear so let me do it here: The potential for a continuous charged object is ##V(\vec{r})=k\int\frac{dq}{|\vec{r}-\vec{r'}|}## and similarily for the electric field. This makes sense outside of the charged object but not inside! Namely, I say it doesn't...

Hello I've been wondering how certain solid state lasers could have a continuous lasing action (Nd YAG laser for instance ) If so,the understanding that the best lasing conditions are when the temperature Is lowest gets disproved(considering that a commendable quantity of heat is produced during...

Hi all, Not sure if this would be the right place for this question, but I know it bothers me for some time already and would really appreciate any kind of help. I am trying to fit an HMM, but here for every observation in the sequence I have feature vector - probability distribution that given...

Let $T$ be a continuous mapping of a complete metric space $X$ into itself such that ${T}^{k}$ is a contraction mapping of $X$ for some positive integer $k$. Then $T$ has a unique fixed point in $X$. Proof: ${T}^{k}$ has a unique fixed point $u$ in $X$ and...

Homework Statement Let X be a compact metric space, F a family of uniformly bounded, equicontinuous real-valued functions on X. Is the function g(x) := supf ∈ F f(x) necessarily continuous? The Attempt at a Solution The hypotheses about the function family seem to point to some use of...

Hello let be $$E = \mathbb{R}[X]$$ with the norme $$||P|| = sup_{t \in \mathbb{R}}e^{-|t|}|P(t)|$$. Let be $$A \in E$$. How to show that $$\Psi_{A} : P \rightarrow AP$$ is not continue please? Thank you in advance and have a nice afternoon:oldbiggrin:.

Hi Readers, I have just began learning about a few types of supersonic wind tunnels. I am more concentrated on the continuous type where the air on the inside can be reused using coolers, fans, vanes, nozzles, diffusers, etc. But can someone give me a few types of these continuous supersonic...

1. Prove that f(x) = \frac{x^2}{1+(x- 1)^2} is uniformly continuous on \mathbb{R}Homework Equations : x^2 - y^2 = (x+y)(x-y) [/B]3. After using the above identity, I am left with |f(x)-f(y)| = |x-y| \left| \frac{x+y-xy}{(1+(x- 1)^2)(1+(y- 1)^2)}\right| and I do not know how to make...

In the lab where I work, we usually use stir/heat plates along with magnetic stir bars to heat our compounds simultaneously. However, in terms of achieving a specific temperature range, the stir/heat plates are not ideally suited due to random fluctuations from being open to the air. Therefore...

haruspex submitted a new PF Insights post Frequently Made Errors in Probability - Continuous and Discrete Distributions Continue reading the Original PF Insights Post.

Hi everyone, First of all thank you for all the amazing amounts of information on this forum! I have a very stupid question, which is probably due to a deep misunderstanding about space quantization. I was wandering why the fact that no mass could move at the speed of light is not per se a...

Hello all, I am wondering if anyone is aware of any continuous processes currently in industry that involve synthesizing some kind of product or material, but takes over 24 hours? I don't mean the entire process itself takes 24 hours or more, but a certain stage of the process, such as the...

Hello! (Wave) Let $V=C^1([a,b])$. Show that if $J$ is a continuous functional in respect to the norm $||y||_1:=||y||_{\infty}+||y'||_{\infty}, y \in V$ then it is also continuous in respect to the norm $||y||:=||y||_{\infty}$. Also, show that the inverse of the above claim does not hold. Let...

I noticed that uniform continuity is defined regardless of the choice of the value of independent variable, reflecting a function's property on an interval. However, if on a continuous interval, the function is continuous on every point. It seems that the function on that interval must be...

jbunniii submitted a new PF Insights post A Continuous, Nowhere Differentiable Function: Part 2 Continue reading the Original PF Insights Post.

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jbunniii submitted a new PF Insights post A Continuous, Nowhere Differentiable Function: Part 1 Continue reading the Original PF Insights Post.

How do i check for correlation or test for association between a continuous data and nominal data in SPSS? My nominal data is the "type of GPS receiver" and the continuous data is "latency" in seconds.

Homework Statement Using continuous beam theory, constructing BM diagram from points b to c, to calculate the max deflection. I only found a have a single solution, though the BM digram show two points of zero bending. I can provide the solution. [edit: Rb = 685 N] Homework Equations...

I am familiar with the explanations for atomic absorption and emission line spectra and how the existence of discrete, fixed energy levels can give rise to the absorption/emission lines that are seen at only very particular frequencies of EM radiation. However, I have no intuitive understanding...

In the plot command below x=1:5:100 plot(x,y,x,0) one plot is noncontinuous zero plot. How can I plot a continuous zero one?

dE = ke(dq/r2) How to change to complicated equation in the following picture?

Homework Statement The problem and its solution are attached in the TheProblemAndSolution.jpg file. Homework Equations E(X) = integral from -infinity to infinity of x * ##f_X(x)## ##f_X(x)## = integral from -infinity to infinity of ##f_{XY}(x,y)## dy The Attempt at a Solution Basically, how...

I'm going through a textbook, on what is pretty much my first course in Quantum mechanics. I've got to a section were it says that in order for a sinusoidal wave function to correspond to a non infinite probability distribution, there must be a range of momentum, or at least more than 1 momentum...

**Motivation:** I am studying for an exam over Chapters $1-3$ of *Real Analysis* by Royden and Fitzpatrick, 4th edition. I am stuck on understanding some of Proposition $11$, which I have reproduced below: **Proposition 11:** Let $f$ be a simple function defined on $E.$ Then for each...