Interval Definition and 677 Threads

Homework Statement Suppose that an investigator believes that virtually all values in the population are between 38 and 70. The appropriate sample size for estimating the true population mean within 2 units with 95% confidence level is approximately how much? Homework EquationsVariance of the...

Hey! I'm working with some regression related stuff at the moment and i'd need some help with multiple variable prediction interval. Prediction interval for a single variable can be calculated using PI = \hat{\beta_0}+\hat{\beta_1}x_i \pm t^* s_e \sqrt{1+\frac{1}{n} +...

Hi guys & girls, I'm using Google maps coordinates to draw a line and want to divide the line by its length, giving segments where the length of each segment is equal to 1. EG: P1 p1.lat = 54.97435323116719 p1.lng = 54.9742647135445 P2 p2.lat = -1.6116368025541306 p2.lng =...

Homework Statement Suppose you have a bucket containing a lot of balls with different colors. You randomly pick 50 balls, 9 of which are red (X = 9, where X ~ N(μ, σ²)). The probability of picking a red ball is 15%. From this you want to construct a 95% confidence interval for the standard...

Let $a$, $b$ be reals and $f: (a,b) \rightarrow \mathbb{R}$ be twice continuously differentiable. Assume that there exists $c \in (a,b)$ such that $f(c) = 0$ and that for any $x \in (a,b)$, $f'(x) \neq 0$. Define $g: (a,b) \rightarrow \mathbb{R}$ by $\displaystyle g(x) = x -\frac{f(x)}{f'(x)}$...

So I was looking at one of the definitions of first order DE's. But I don't get what this statement means: let a function f(x) be defined on an interval I.

Homework Statement Suppose X1, X2, ..., Xn constitute a random sample from a population following N(μ,θ) where μ is known. (a)Find a sufficient statistic for θ. (b)Use the maximum likelihood estimator of θ to construct a confidence interval for θ with confidence level 1-α. Homework...

Our task is to determine if P(-c \le X \le c) has a minimum variance unbiased estimator for a sample from a distribution that is N(\theta,1). The one-sided interval P(X \le c) = \Phi(x - \theta) is unique, so constructing an MVUE is just a matter of applying Rao-Blackwell and Lehmann-Scheffe...

"Find x_0 and the largest interval, I, for which y(x) is a sol[...]" Homework Statement Given that y = –2/x + x is a solution of the differential equation xy' + y = 2x, find ##x_0## and the largest interval, I, for which y(x) is a solution of the initial-value problem: xy' + y = 2x...

Hello! :) I am given the following exercise: Which integers of the interval: $[-100,400]$ have the identity: divided by $11$,the remainder is $2$ and divided by $13$,the remainder is $3$. It is like that: $[x]_{11}=[2]_{11} \Rightarrow x \equiv 2(\mod 11) \Rightarrow 11 \mid x-2 \Rightarrow...

Homework Statement infinity ∑ (x^(n+5))/3n! Find the radius of convergence and interval of convergence n=0 Homework Equations The Attempt at a Solution I got 0 for the radius and 0 for the interval of convergence using the ratio test. This is no right. Can someone please help me? Thank you

Homework Statement So I solved this problem ∑ (-1)^n (x+5)^n by finding the sum of the series to be 1/(x+6), which was correct. I am stuck on the second part of the problem asking for interval notation. It says: Determine, in interval notation, the values of x for which the series converges...

Homework Statement What does it mean? Is this the interval such that 95% of the means from a sample mean distribution (frequency distribution of means of sample size n) are a certain number of standard deviations from the population mean? Homework Equations The Attempt at a Solution

How would I find the interval of convergence for the following series: i) $$\sum \frac{(x+2)^n}{n^2}$$ ii) $$\sum \frac{(-1)^kk^3}{3^k}(x-1)^{k+1}$$ iii) $$\sum (1+\frac{1}{n})^nx^n$$ Reason for edit: My second series was not displaying properly

The distribution of grades is know to follow a normal distribution, but the mean and variance are unknown. A random sample of 12 students produced the following scores: 59, 84, 68, 93, 49, 77, 82, 75, 81, 58, 70, 80 Find the 90% two-sided confidence interval for the mean score.

If the space-time interval is calculated according to: ds2=dx2+dy2+dz2-c2*dt2 what might be an example of 2 events in space-time separated by this interval? Suppose for example ds2 =1 (or a constant) and the first event was at the origin where would the second events lie? Am I...

Homework Statement Find the conditional distribution function and density for the random variable X defined on R given that X is in some interval I = (a,b) where P(X in I) > 0. Assume that the density and distribution for the random variable X is known Homework Equations fX|X\inI =...

Let ##I## denote the interval ## [0, \infty )## . For each r ## \in I ## define: ##A_{r} = \{ (x,y), \in ##R x R : ## x^{2} +y^{2} = r^{2} \}## ##B_{r} = \{ (x,y), \in ##R x R : ## x^{2} +y^{2} \leq r^{2} \}## ##C_{r} = \{ ## ... ## : ... > r^{2} \} ## a.)...

For a simple linear model: \alpha+\beta\times x=y If it is observed that y \in (-8.51,23.20) given x=4 The question is to give intervals of \alpha, \beta, which satisfy y \in (-8.51,23.20) given x=4. Is this problem identifiable? Can it be found the unique intervals for \alpha...

Homework Statement I am confused about how they got the expression: VPcos(ωΔt)=VP-Vr Specifically you can find the notes in page 5 of this article: http://whites.sdsmt.edu/classes/ee320/notes/320Lecture8.pdf You may also find it useful to refer to the graphs as a reference...

Homework Statement A machine fills cereal boxes, normally distributed, with standard deviation of .1 oz. What amount setting should the machine be set to if only 1% of the boxes can have less than 16oz of cereal? Homework Equations The Attempt at a Solution I am thinking that I...

See attached for problem Working: Mean: 1203.26 Standard Deviation: 7.047 for 99% confidence interval, level of significance = 0.01 Therefore 0.5 - 0.01/2 = 0.45 Reading 0.45 from standard distribution table i get a value of 1.65 therefore confidence interval should be...

I have a bunch of noisy data points (x,y), and I want to model the data as y = ax2 + bx + c + noise where noise can probably be assumed to be Gaussian, or perhaps uniformly distributed. My data is firmly inside of an interval and I'm only interested in modeling correctly inside of this...

In special relativity we have the invariant spacetime interval ds2 = dx2 - c2dt2. If we think about classical (non-relativistic) space and time as one spacetime in which the transformation between reference frames is given by the Galilean transformation, is there a corresponding spacetime...

Homework Statement serie ((-1)^(n-1)(x-2)^(n-1))/(5^n) Homework Equations how to find the interval of convergence for this? The Attempt at a Solution

Hello May I know what is the difference between Confidence Interval for Population Mean (μ) when σ Known vs Confidence Interval for Population Mean (μ) when σ unknown.. any example to show me??

What is ds^2 on a rotating disk?

Can anyone please give a succinct and clear description on this? I'm a little confused...

Hello, I need help using my TI 84 to figure out this 4 part question. My professor went over it way to quickly in class, when showing us how to do it on the TI 84, I believe its only a few quick steps for each part though. EDIT: I have figured out part d, but am still struggling with parts a...

Hi! My question is: Find maximum and minimum values of the function: f(x,y) = 2x-y+x^2+y^2 when x^2+y^2 ≤ 4 I would like to solve this without using Lagrange method. I get x=-1 and y=1/2 when using partial derivative and set it equql to 0. I can see that the maximum value...

Homework Statement We are given ##H## = {##O | \forall x, \exists a,b \in R## s.t ##x \in [a,b] \subseteqq O##}##\bigcup {\oslash}## and are asked to show that it is a topology on R Homework Equations Definition of a topological space The Attempt at a Solution I am trying to...

Homework Statement Find the radius of convergence and the interval of convergence Homework Equations A_n = Ʃ sum n =1 to infinity [((-1)^n) x^(2n+1)]/(2n+1)! The Attempt at a Solution All I thought was to use the ratio test so I did A_(n+1) /A_n = ((x^(2n+1))/(2n+1)!) (...

I know y is a function of x [i.e. y=f\left(x\right)] with two known boundary conditions, that is f\left(x=A\right)=C and f\left(x=B\right)=D where C and D are known constants (please see figure). I do not know the form of this function and therefore I am trying to find the form of y as a...

I have a problem on which I need to apply Euler's method - EXCEPT that I don't have one of the crucial components. Question and my thoughts below: **Question:** Consider the initial value problem $\frac{dy}{dt}=\alpha t^{\alpha - 1}, y(0)=0$, where $\alpha > 0$. The true solution is...

Prove that the interval A = [0 , 2) has the same cardinality as the set B = [5 , 6) U [7 , 8) by constructing a bijection between the two sets Attempt: x ↦ x + 5 for x ∈ [0 ; 1) x ↦ x + 6 for x ∈ [1 ; 2) What to do next?

A researcher surveys 25 people and finds that their average commute is 15 minutes with a standard deviation of 1.5 minutes. Calculate the 95 percent confidence interval on variance. Do most people have a commute of 20 minutes? Confidence interval for variance? should I just use the variance...

Homework Statement i have solve 7sin(2x)-13sin(x)=0 for all solutions 0≤X<2p I used the double angle formula for sin(2x)=2sin(x)cos(x) The Attempt at a Solution I'm getting stuck near the end 7(2sin(x)cos(x)-13sin(x)) 14sin(x)cos(x)-13sin(x) now I am stuck

I have a problem: the radius of convergence for the power series \sum(-1)^n \frac{(x-3)^n}{(n+1)} is R=1. Determine the interval of convergence. What does this mean? can anyone help me solve this please

Find an interval centered about x=0 for which the given initial value problem has a unique solution. (x-2)y''+3y=x where y(0)=0 and y'(0)=1 I've seen the answer on a few different sites (1)(2) and still don't get it :mad: The question speaks of a unique solution with regards to an interval...

Here is my question: Solve the initial value problem \(y\prime=\dfrac{3x^2}{3y^2-4},~y(1)=0\) and determine the interval in which the solution if valid. Hint: To find the interval of definition, look for points where the integral curve has a vertical tangent. My work so far...

Homework Statement http://i.minus.com/jbiWoIFy45kCgV.png Homework Equations The denominator of a function cannot equal 0. Both the numerator and denominator also cannot = 0 simultaneously. The Attempt at a Solution For the first problem, the denominator and the numerator are 0...

Homework Statement Hi guys! I must show by brute force that ##\Delta s^2=-c^2\Delta t^2+\Delta x^2+\Delta y^2+\Delta z^2## is invariant under Lorentz transforms. Homework Equations Lorentz transforms: ##\Delta t' = \gamma \left ( \Delta t -\frac{\vec v \cdot \Delta \vec x}{c^2} \right...

The course this question comes from is Modern Physics Homework Statement What is the proper time interval between two events if in some inertial reference frame the events are separated by 109m and 5s? Homework Equations I looked through my notes and under a the sub topic "Invariant...

I hope this makes my question clear... suppose we have a triple integral of dzdydx for [0<x<1 , sqt(x)<y<1 , 0<z<1-y] and from the sketch we can see that 0<y<1 and 0<z<1... my question is this, if we change the integration to dzdxdy we get [0<x<y^2 , 0<y<1 , 0<z<1-y], is that the only way? or...

Homework Statement The left side in the equation \sqrt{3-x}\sqrt{x+9}=8x+1 is only definable when x is located in a certain interval a \leq x \leq b. What's a & b? (Note: The answer ought to be integers) The Attempt at a Solution \sqrt{3-x}\sqrt{x+9}=8x+1 (\sqrt{3-x}\sqrt{x+9})2=(8x+1)2...

Homework Statement Particle is in an infinite square well of width ##L## on an interval ##-L/2<x<L/2##. The wavefunction which describes the state of this particle is of form: $$\psi = A_0\psi_0(x) + A_1\psi_1(x)$$ where ##A_1=1/2## and where ##\psi_0## and ##\psi_1## are ground and first...

Homework Statement Find the interval of convergence for the following power series. Specify both absolute and conditional convergence where appropriate.Homework Equations 1 + x + 2x^2 + 6x^3 + ... + n! x^n + ...The Attempt at a Solution Using the ratio test to determine convergence of the...

I haven't found a comparison like this in any book that I have been reading so let me explain. I decided that I will derive an equation for an energy levels of a particle in an infinite potential well in two ways. 1st I tried to derive it using the interval ##0<x<d## where ##d## is a width of...

I am currently working on a prediction problem using generalized linear model, My goal is to get the prediction distribution of the response variable. I read a thread (https://stat.ethz.ch/pipermail/r-help/2003-May/033165.html) saying the prediction uncertainty of a generalized linear model...

x^n/(2n-1) is the series. It starts at 1 and goes to infinity. I did the ratio test on it and got abs.(x) So the radius of convergence=1, and then I plugged -1 and 1 into the original series and got that they both converged. But the answer is [-1,1). Why aren't they both hard brackets?