Independent Definition and 713 Threads

Say I have an urn containing a set of balls numbered 1 through N. I then make n selections from the urn with replacement. Thus each selection is independent. Let the event: A_{i} i=1,2,3...,N be that the ball numbered i was not chosen in the n selections. Then...

Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks!

Homework Statement V = { (x_{1},x_{2},x_{3},x_{4},x_{5}) \in R^{5} : x_{1} -2x_{2} + 3x_{3} - x_{4} + 2x_{5} = 0 } show that S = { (0,1,1,1,0) } is a linearly independent subset of V. The Attempt at a Solution I don't get it.. it's a set with 1 non zero vector, it's going to be...

Homework Statement Let X and Y be independent and normal, then we know that It must be the case that X+Y and X are jointly normal Therefore we can apply the projection theorem: which states that if A and B are jointly normal then VAR(A|B)=VAR(B)-\rho^2VAR(B) , apply the theorem to A=X+Y, B=Y...

I can understand that if z= a + ib then z*=a - ib, where the definition of the complex conjugate is reversing the sign in front of the imaginary part. I'm now confused about how the complex conjugate works in the TISE. in a stationary state, i\hbar\frac{\partial\Psi}{\partial\\t}= E\Psi...

Vector and matrices...are the independent or dependent Homework Statement Determine whether the vectors v1=[1,-1;0,0],v2=[2,-2;1,... and v3=[-5,5;1,0] are independent or dependent. Find the span {v1,v2,v3} and give a description. Explain why W = [4,4;4,4,] is not in the span {v1,v2,v3}...

Homework Statement Determine whether the vector v1=(!,2,3),v2(3,2,1) and v3(1,1,1) are independent or dependent. Homework Equations I'm so lost The Attempt at a Solution I'm so lost

Hi, everyone: I was reviewing some intro material, and I ended up confused with the issue of independence with the following problem: We are given two teams, A,B, playing against each other. A wins with probability P(A)=0.6 , B wins with P(B)=0.4 (games are played until...

I am a little fuzzy on the meaning of Independent Identically distributed random variables. I understand the independent part but still not 100% on the identically distributed part. I understand that identically distributed means they have the same pdf and cdf but does this mean that they have...

Number of "independent" subcubes of a hypercube Hello, I am trying to solve this problem: I have an n-dimensional hypercube and m of its vertices. Now I want to compute the maximum number of subcubes of the entire hypercube such that: - each subcube from the set may contain only those m...

Homework Statement Let S be the sample space for rolling a single die. Let A={1,2,3,4}, B={2,3,4}, and C={3,4,5}. Which of the pairs (A,B), (A,C), and (B,C) is independent? Homework Equations P(A|B)=P(A) P(A|B)=P(A&B)/P(B) P(A&B)=P(A)*P(B) The Attempt at a Solution P(A)=2/3...

Homework Statement Hi there, I'm doing a practical investigation to see how the centripetal force required for circular motion varies with the frequency of rotation, and I was just wondering which is the independent variable, and which is the dependent one. The investigation involves...

Homework Statement Suppose that A, B, and C are not linearly independent. Then show how the \alpha_{i} can be computed, up to a common factor, from the scalar products of these vectors with each other. Hint: Suppose that there are non-zero values of the \alpha_{i}'s that satisfy...

Homework Statement So I'm trying to find a basis for the space that is spanned by the given vectors. {(1,0,0,1) (-2,1,-1,1) (6,-1,2,-1) (5,-3,3,-4) (0,3,-1,1)} These are written as column vectors. Homework Equations None really (that I know of) The Attempt at a Solution So I...

Homework Statement Were the columns of A linearly independent? The matrix A is given in row reduced echeleon form 1 2 0 0 0 0 1 0 0 0 0 1 Homework Equations Hint: Consider the solution set to A x = 0 The Attempt at a Solution I think that the...

Let x1, x2,...,xk be linear independent vectors in a vector space V. If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain. By deleting a vector from linearly independent span, the other vectors, I believe, will remain...

Let x1, x2,...,xk be linear independent vectors in a vector space V. If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain. By deleting a vector from linearly independent span, the other vectors will remain independent...

In short, I think I may want to spend either next semester or all of next year at the Independent University of Moscow, but I've only really decided this recently. I haven't spoken to my university, asked for recommendations yet, or filled out the application form, and all of this must be...

Homework Statement Two cards are drawn from a standard deck with replacement. A=first card is an ace. B=second card is an ace. Show that A and B are independent Homework Equations P(A and B)=P(A given B)/P(B) P(A given B)=P(A) The Attempt at a Solution P(A)=4/52 P(B) =4/52 P(A...

Say I have a packet of electrons just sitting there, before they repel each other, what is their potential energy? I have no idea of how to calculate their potential energy since at r = 0 , U = infinity, which is not helpful since my problem requires U to be finite but the only way I know of...

Standard Matrix for R^3 -> R^4 where if domain is Linearly Independent so is codomain Homework Statement 5. Suppose T : R^3 -> R^4 is a linear transformation with the following property: For any linearly independent vectors v_1, v_2 and v_3 in R^3, the images T(v_1), T(v_2) and T(v_3) are...

Homework Statement Among all independent vector sets in a vector space U, let M = {v1, v2, ... vp} be an independent set. p is as large as it can get. Show that U is a basis of M. Homework Equations The Attempt at a Solution If U is a basis of M then U is an independent set (we...

What is it meant by "mass-independent renormalization scheme"? Does it mean that the counter-terms that cancel the infinities do not have dimensions of mass? In this case, any regularization scheme not involving the cutoff method, such as dimensional regularization? Or does it mean that...

Hi, I am attempting a logistic regression analysis with a binary response and explanatory variables measured at the individual level and also some measured within subgroups of the observations (nests). For each nest containing individual observations I know the distribution of income in the...

Is there any physical reason why second order approximation to ground state in time independent perturbation theory is always negative. I know how to prove it mathematicly but I wonder whether one may justify it using only physical arguments.

I am currently a senior in high school and I am working towards a career which involves the study of physics. I am somewhat aware of independent research opportunities for high school students in other areas of science, but I do not know of any opportunities which I could explore for physics...

Through our research we discover that an AC induction motor can act as a DC amplifier, as long as there is torque making it turns. Applying the process we are able to build RPM independent grid tie induction generator. Tested with variable US grid at consumer configuration. Similar to PMA...

Hello, I'm using UV-C (Hg low pressure lamp) and I wanted to see if someone could give me some insight. I have a couple of questions: 1) How far does UV-C penetrate through various materials? In my testing, it seems to go straight through plastics. I have UV blocking glasses - but those are...

Let X1, X2, ...Xn be independent exponential variables having a common parameter gamma. Determine the distribution of min(X1,X2, ...Xn). The Attempt at a Solution I know how to do it with one X and one parameter but I am at a loss with these multiple ones... Thanks so much!

I am interested in describing the heat transfer and temperature gradients within a mixture of independent radiating bodies. States like this occur in many systems and i have been having a bit of trouble modeling this simple scenario. An example of a system is charcoals within a BBQ, and also...

I'm currently in the first year of my undergrad, and want to pursue Physics independently of the main Physics course. So I need to know what topics, AND IN WHAT ORDER, do I need to study to get a systematic knowledge of up to, say, Quantum Electrodynamics. (Undoubtedly this will take some...

Homework Statement There are two urns, A and B. Let v be a random number of balls. Each of these balls is put to urn A with probably p and to urn B with probability q = 1 - p. Let v_a and v_b denote the numbers of balls in A and B, respectively. Show that random variables v_a and v_b are...

I am looking for a Hoeffding-type result that bounds the tail of a sum of independent, but not identically distributed random variables. Let X_1,..,X_n be independent exponential random variables with rates k_1,...,k_n. (Note: X_i's are unbounded unlike the case considered by Hoeffding) Let S=...

Here's a stupid question: for a Gaussian process, are these two properties equivalent?

If x and y are independent and identically distributed exponential random variables, and z = x+y w = x-y are z and w also independent? Do I have to actually find the joint pdf of z and w, then find the marginals and then see if they multiply to equal the joint pdf? Or is there a way to just...

I have a quick question about vector spaces. Consider the vector space of all polynomials of degree < 1. If the leading coefficient (the number that multiplies x^{N-1}) is 1, does the set still constitute a vector space? I am thinking that it doesn't because the coefficient multiplying...

Independent Probability... Hello, Could someone point me in the right direction of how to prove that P(A|B) = P(A) if and only if P(B|A) = P(B)? I think I understand the program and I can't formulate any contradictions, but I'm having difficulty showing this property with a formal proof...

Is it possible to become an "independent" physicist? Greetings all. I've read lots of threads on here about "old" guys (the poster is usually 29 or 30) going back to school to study physics, and I've digested the oft-repeated issue of no jobs in academia even for young guys, let alone oldsters...

For a gas that obeys the equation of State P(v-b) = RT, where b is a constant, show that Cp is independent of Pressure, i.e., (\deltaCp/\deltap) at constant T is equal to zero Homework Equations Maxwell Relations H = U+PV dh = TdS + PdV dh/dT at constant P is defined as Cp The...

Help! I am losing my mind over this problem (which is basically problem 2.6.5 in Arfken and Weber Mathematical Methods for Physicists, sixth edition). I am having difficulty using the tensor symmetric and antisymmetric relationships of the Riemann-Christoffel tensor to show that it reduces...

Let A1,A2, . . . ,An be subsets of . Show that if A1,A2, . . . ,An are independent, then the same is true when any number of the sets Ai are replaced by their complements (Ai)c. (Hint: First do the case in which just one of the sets is replaced by its complement. Then argue by induction on...

Homework Statement Vicki owns two separtment stores. Delinquent charge accounts at store #1 show a normal distribution, with mean $90 and std. deviation $30, whereas at store #2, they show a normal distribution with mean $100 and std. deviation $50. If 10 delinquent accounts are selected...

hey guys, tell me how i would approach this: a communication system sends signals from 'a' to 'b' over 2 parallel paths. If each path has 2 repeaters with failure probablities X for the first path repeaters ,Y for the second path repeaters then what would be the probability of signal not...

I am a high school senior and am enrolled in an independent study class, but am having a difficult time finding a topic for my research... Does anyone have any suggestions or links to any sites that could help me find one?? I plan on studying physics in college and would like to keep it...

Homework Statement The distribution of the IQ of a randomly selected student from a certain college is N(110,16). What is the probability that the average of the IQ's of 10 randomly selected students from this college is at least 112? Homework Equations I think we need P(Sample Mean...

Hello, What is the difference between independent and uncorrelated random variables? Practical examples of both? Regards

Homework Statement Considering the following vectors R^{4}: v1 = (1,2,0,2) v2 = (2,3,1,4) v3 = (0,1,-1,0) Determine if these vectors are linearly independent. Let S be the linear span of the three vectors. Define a basis and the dimensions of S. Express the vector v=(3,5,1,6) as a linear...

I am having an awful time trying to find a topic... any help would be appreciated

Why is the speed of light constant and independent from the observer?

one of the laws of friction states that the frictional force is independent of the area of contact,and velocity,how true is this? my book says this particular law is only approximately true.