Independent Definition and 745 Threads

Jeeserssweesers(for a lack of a better word), probability is confusing. Homework Statement A family has three children, no twins or.. that same just with three. a| What is the chance that all the children are girls. Homework Equations The chapter here shows the equtations...

uh, I mean probability with independent outcomes, heh. Homework Statement A wheel I'm spinning twice has 8 different colours(among them the colour red). It will then give two different outcomes. Q: What is the probability that the outcome will give the colour red at least once. The...

Hi I have a question regarding i.i.d. random variables. Suppose X_1,X_2,\ldots is sequence of independent and identically distributed random variables with probability density function f_{X}(x), mean = \mu and variance = \sigma^2 < \infty. Define Y_{n} = \frac{1}{n}\sum_{i=1}^{n}X_{i}...

Why does this work?? (X and Y independent) There is an image attached to refer to my question. A ballistics cart traveling at constant velocity can shoot a projectile straight into the air and the projectile will be caught in the car when it lands because of the independence of the X and Y...

Homework Statement Given x_{1}= \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, x_{2}= \begin{pmatrix} 3 \\ -1 \\ 4 \end{pmatrix}, x_{3}= \begin{pmatrix} 2 \\ 6 \\ 4 \end{pmatrix} Find the dimension of Span(x_{1}, x_{2}, x_{3}) Homework Equations If V is a vector space...

Hi Ho! If y=\sin x, \frac{dy}{dx}=\frac{d(\sin x)}{dx}=\cos x. If x=\sin y, y=\arcsin x, and therefore \frac{dy}{dx}=\frac{d(\arcsin x)}{dx}=\frac{1}{\sqrt{1-x^2}}. But, if x=\sin y, can \frac{dy}{dx} be done as \frac{dy}{dx}=\frac{dy}{d(\sin y)}=\frac{1}{\frac{d(\sin...

Homework Statement A particle of mass m and energy E, where E >V1 >V2 travels to the right in a potential defined as V(x) = V1 for - b < x < 0 V(x) = 0 for 0 < x < a V(x) = V2 for a < x < b (a) Write down the time-independent Schrodinger eq. and its general solution...

Show that the evaluation of the pullback of a constant 1-form k_{1}dx + k_{2}dy + k_{3}dz over the directed line segment from \bold{r} to \bold{s} does not depend on which linear parameterization is chosen. So (x,y,z) = \bold{r} + t(\bold{s}-\bold{r}) . Then what?

Apparently next week, Kosovo, the small southern povince of Serbia is set to declare independence, which will become a reality if the EU and US recognize it. Of course, Serbia and Russia disagree. In Kosovo, it's 'Independence Eve'...

Hi all, assume we have a sample space with 2^n points. (it size is 2^n for some natural n) I need to prove that the maximal number of independent binary (indicator) random variables (which are not trivial, i.e. constant) is n... Thnks, Pitter

I'm not sure how to get started with this: Suppose you have two independent poisson processes, X ~ Po(Lambda1) Y ~Po (Lambda2). How would you figure out the probability of one coming before the other? Thanks

Say f is a continuous function on R. How could I find two linearly independent solutions of (y' + f(x)y)' = 0? Notice that there is no hypothesis about f being differentiable, so the obvious method of attack (taking the derivative of each term in the parenthesis and working off the resultant...

[SOLVED] Change of independent variables Homework Statement x = cos\theta Show (1-x^2)\frac{d^2y}{dx^2} - 2x\frac{dy}{dx} + 2y = 0 becomes \frac{d^2y}{d\theta ^2}+ cot(\theta) \frac{dy}{d\theta} + 2y = 0 Homework Equations The Attempt at a Solution dx = -sin(\theta) d\theta ... As a total...

[SOLVED] QM: system with two lin. independent states Homework Statement Imagine a system with just two linear independent states: |1>=(1,0) and |2>=(0,1) (these are actually column matrices, but I don't know how to type those in tex) |\Psi>=a|1>+b|2>=(a,b), also |a|^2+|b|^2=1 suppose the...

independent research - hockey Homework Statement I have been assigned a physics project to do over the break. I need to research the design and use of a piece of protective equipment - I have decided on hockey equipment. 2. The attempt at a solution The most obvious feature is that the...

I have a final tomorrow. Can anyone guide my through this proof? I know i have to wirite the set of vectors as a linear combo, but what can I do nect? Prove that any set of vectors containing the zero vector is linearly dependent.

qestion regarding independent study! Hi everybody! Next semester i am taking the university physics 203 along with linear algebra and differential equation. In the physics class we are studying basic optics, thermodynamics, waves, introductory relativity, and basic modern physics. Although...

Homework Statement In a testcross in D. melanogaster, the female heterozygote shv+/shv ; he+/h+e is crossed to a male from the homozygous recssive stock, shv/shv ; he/he. What proportion of the hairy-bodied flies has short veins? What event during meiosis causes this? How does the...

When we say that the the velocity of light, c, is independent of the velocity of emitter or the observer, does it mean that .. if we are in an spaceship and measure c with Fizeau arrangement we will obtain the same result, no matter the velocity of the spaceship nor the velocity of the...

How do you see things shaping up during the next few years in Quantum Gravity? the last two years have seen a lot of change there are some new approaches that have either just been discovered (like Smolin's group finding matter degrees of freedom in spin networks) or have recently become...

H=H0 + lambda * W lambda << 1 must hold and the matrix elements of W are comparable in magnitude to those of H0. More precisely, the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0. I don't understand what is the meaning of " the matrix...

Homework Statement Let X,Y be two independent normal N(0,1) and N(0,2) variables, and Z=XY. Suppose that E(X^4)=3 a) Compute Var(X), Var(Y), Var(Z), Cov(X,Y), Cov(Y,Z), Var(X+Y), Var(X+Z) b) By computing E[(X^2)(Z^2)], prove that X,Z are not independent.Homework Equations Var(X)=E(X^2)-E(X)^2...

H=H0 + lambda * W lambda << 1 must hold and the matrix elements of W are comparable in magnitude to those of H0. More precisely, the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0. I don't understand what is the meaning of " the matrix...

Homework Statement Let C_n Recalling our notation from class, we know that I_0(C_n) = 1 and I_1(C_n) = n. Prove that for k > 1, I_k(C_n)=\left(\frac{n}{k}\right)\left(\stackrel{n-k-1}{k-1}\right) Homework Equations I_k implies number of independent sets of size k C_n implies the cycle with...

http://garciarussellchem.angelfire.com/Photo/Change_of_independent_variables_problem.jpg Homework Statement Homework Equations See Image at above adress The Attempt at a Solution See image at above adress

This is my second class in intro to probability at a university level. 1) There are 5 people in a room with 3 boys and 2 girls. If I randomly pick 1 person from the box, P(boy)=3/5. If I randomly pick 2 people, P(pick 2 girls) = 2/5 x 1/4 = 1/10. a) Now what is P(pick 1 girl and 1 boy)...

Right now I'm doing Centroids in my math class. we are given two functions. X=-y and X=2y-y^2. My question is, how do I graph these two functions on my TI-89 titanium. The Y=editor is displayed as y(x). Is there a way to change it to X(y). I was able to plot it out on paper, but I use...

Homework Statement Is {(1,4,-6), (1,5,8), (2,1,1), (0,1,0)} a linearly independent subset of R^3. Justify your answerHomework Equations The Attempt at a SolutionI asssumed a(1,4,-6) + b(1,5,8) + c(2,1,1) + d(0,1,0) = 0 then i set up the system a + b + 2c = 0 4a + 5b + c + d = 0 -6a + 8b + c...

Is there any theory of information that considers a 'bit' to be something that only exists relative to a pair of systems exchanging information? I.E there is no such thing as an isolated 'bit'.

Are the functions y=0 and y=sinh(pi*x) linearly dependent or linearly independent on the intercal x>0? I'm not sure what I'm supposed to do here, but I try to divide them: 0/sinh(pi*x). This is certainly 0, since sinh (pi*x) is positive when x>0. Since 0 is a constant, the functions must...

I'm looking ahead to winter quarter 2008 when I will be starting an independent research project. I wanted to get an early start in thinking about what I might be able to do. I am thinking that I want to do something in signal processing, but don't have enough knowledge to make a choice. Here...

Dear all, I wonder wheather there exsits a probability inequality for the sum of independent normal random variables (X_i are i.i.d. normal random varianble with mean \mu and variance \sigma^2): P\left(\frac{1}{n}\sum_{i=1}^n X_i - \mu> \epsilon\right)\leq f(\epsilon, \sigma^2,n) \right). We...

Hi everybody, I am currently at a summer program hosted by my home state of Georgia (USA) called the Governors Honor's Program. Right now we are preparing for our final project that's supposed to take up the remainder of our time here (roughly three weeks). My partner and I are supposed to...

hey everyone, I first started doing independent research myself, exploring topics myself, but how do I do "offical" research that counts towards college admissions (I am a high school student by the way). Thanks

I'm currently reading Griffith's book on time independent Schroedinger's equation about delta functions. However, I complete dislike how the book deals with the delta distribution. firstly, the book discusses how to solve: -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2}-\alpha\delta\psi=E\psi for...

Is this a valid thing for society to aim for? Would this do more harm than good? Technology is capable of taking us towards this.

I have looked all over in many textbooks and I cannot find a decent explanation of this. Most textbooks simply say that it is independent of applied bias because all of the minority carriers generated by thermal energy within a diffusion length of the depletion region will essentially get swept...

Question: Prove that the list (x^3, sin(x), cos(x)) is linearly independent in V (V being the vector space of real-valued functions. In other words... common everyday math) They're linearly independent, its pretty obvious. The issue is -- proving rigorously. This is not for an assignment, its...

I’m student at the University of Arizona. In my political science class, I need to use SPSS to calculate bivariate correlation between a categorical independent variable (Presidential or Parliamentary system) and a continuous dependent variable (various measures of democracy) I’m using the...

"Independent Continuum" Can anybody please explain to me what this actually means. My understanding in very vague terms is that something is constant, with reference to Einstein's The Special and General Theory book, where he says that we often think of time (and space i think) as "independent...

Marcus! Your find... http://arxiv.org/abs/gr-qc/0703097 New directions in Background Independent Quantum Gravity Fotini Markopoulou Perimeter Institute for Theoretical Physics Good stuff. How influential is Fotini Markopoulou? Is anybody going to listen? jal

Hello, I am not sure if this is the right place to ask this, but I don't readily see a "numerical methods" forum here so I assumed this would be the place to go. Sorry if I overlooked another place to post this! Anyway, I have some points interacting via potentials that are dependent only on...

Homework Statement Let \mathscr{X} be a set, \mathscr{F} a \sigma-field of subsets of S, and \mu a probability measure on \mathscr{F}. Suppose that A_{1},\ldots,A_{n} are independent sets belonging to \mathscr{F}. Let \mathscr{F}_{k} be the smallest subfield of \mathscr{F} containing A_{1}...

let V be a vector space and K a nonempty subset of V prove/disprove : K is linear independent set iff for every T such that T is a proper subset of K, span(T) is a proper subset of spanK. im having difficulty finding a counter example, so i think this statement is correct, but how to prove...

Is the Doppler shift an independent principle of wave mechanics? Or we can deduce it from other principles of wave mechanics? The article [1] gives an analogy of throwing and receiving balls. But it may be inappropriate. We are discussing wave mechanics? Why bother an analogy of balls/particles...

My teacher gave these notes: In general, if any two events A and B we find that Pr(B|A)=Pr(B), or equivantly, Pr(AnB)=Pr(A)Pr(B), then the events A and B are independent. but i thought that when A and B are independent then Pr(AnB)=0? what is my teacher trying...

A friend gave me this problem; it's been years since I've taken probability, and I'm really rusty. I'm curious how to solve it. Suppose you have a normal pdf with mean mu and stdev sigma that represents the distribution of test scores. What's the probability that two randomly selected...

Silly question of very little importance :smile: My dad just asked me the following question: You have 10 standard independent decks (52 cards), you draw 1 card from each deck 1 at a time, what is the probability (count) of getting 4 aces (not necessarily distinct suits) out of the 10 cards...

I found this post somewhere on the net. I am also getting a similar problem. Can you all please help? +++++++++++++++ I have a problem, I try to solve but still get stuck. Can you please read my solution and point out what my wrong points are? Xn is a Markov Chain . n=1...M. with...

I'm having trouble understanding what to do for this problem. The question I'm trying to answer is: Find 3 linearly independent solutions to the following differential equation, y^(3) + 3y'' + 3y' + y = 0. I really don't know how to even start this problem and what I'm really looking for. I...