Independent Definition and 745 Threads

Homework Statement Suppose X1 and X2 are two independent gamma random variables, and X1~Gamma(a1, 1) and X2~(a2, 1). a) Find the joint pdf of Y1 = X1 + X2, and Y2 = X1/(X1 + X2). b) Show that Y1 and Y2 are independent. c) Find the marginal distributions of Y1 and Y2. The Attempt...

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...

When talking about the translational velocity of a rigid body in physics, the velocity is always frame dependent, and therefore, the translational kinetic energy is frame dependent. But does this apply to angular rotation phenomenon? If in one frame, the angular velocity of a rigid body is 10...

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 Let X be the height of a man and Y be the height of his daughter(both in inches). Suppose that the joint probability density function of X and Y is bivariatenormal with the following parameters: mean of X=71, mean of Y=60, std. deviation of X=3, Std. deviation of Y=2.7...

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?

Homework Statement Let (A_n) be a sequence of independent events such that Pr(A_n)<1 for all n. Show that P[limsup A_n]=1 if and only if P(\cup_{n=1}^{+\infty} A_n)=1 Homework Equations The Attempt at a Solution Suppose P[\limsup A_n]=1. Define $B_k=\cup_{i=k}^{+\infty} A_i so...

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.

Homework Statement In the space of 2 by 2 matrices, find a basis for the subspace of matrices whose row sums and column sums are all equal. (Extra credit: Find five linearly independent 3 by 3 matrices with this property) The Attempt at a Solution The first one is ok. The matrix is...

1 Let X be a normal variable with mean 0 and variance 1. Let Y = ZX where Z and X are independent and Pr(Z = +1) = Pr(Z = -1) =1/2. a Show that Y and Z are independent. b Show that Y is also normal with mean 0 and variance 1. c Show that X and Y are uncorrelated but dependent. d Can you...

I was wondering how complex would it be to determine the maxima-minima extrema for a 6 independent variable function? I am assuming it might be enormous if not untenable being that it is all done in "hyper-space" and neither the dependent or all 6 of the independent variables could be visually...

hello guys, am new to pf. am a post graduate student of university of glamorgan, studing geographical information system. am currently doing an idependent study on the monitoring of glaciers using remote sensing.am trying to do an analysis(ndsi- normalised difference snow and ice index) on some...

Homework Statement If S = {v1, v2, v3} where v1, v2 and v3 are in \mathbb{R}^2, then the vectors v1, v2 and v3 are linearly independent. Homework Equations NoneThe Attempt at a Solution I thought the answer was true, but I know the correct answer is false and I'm not sure why. Here was my...

simple harmonic motion --> amplitude independent of mass? I know that acceleration is directly proportional to displacement, but opposite in sign, and that acceleration and displacement are related by the square of the frequency. But i was wondering if amplitude is independent of mass in...

Hi, I am confused with respect to these two terms. In a book on regression analysis, I read the following statements. 1. For two normally distributed variables, zero covariance / correlation means independence of the two variables. 2. With the normality assumption, the following...

Homework Statement normalize the wave function \Psi(x)= Acos(\Pi*x/a) to show that A=\sqrt{2/a} The Attempt at a Solution i don't know how to get that answer as all i can tell, normalizing gives: -A^{2}pi^{2}2x/a^{2} * sin (pix/a) However this does not give the right answer for A Any...

There's a PDF attached to this; have I concluded things the right way?

Hi all, I have been studying Linear Algebra for an upcoming exam, and one question has puzzled me slightly! How do you determine of a vector in R4 is linearly independent? Given three vectors, each with 4 rows, I know you are meant to arrange them into a matrix, like this: \[ \left(...

Because according to my book, If A's an invertible nxn matrix, then the eq. Ax=b is consistent for EACH b... this consistency would imply lin. independency?

Homework Statement Suppose that {v1,...,vn} is a linearly independent set in a vector space V and let L:V --> W be a one-to-one linear mapping. Prove that {L(v1),...,L(vn)} is linearly independent. Homework Equations None The Attempt at a Solution If L is a one-to-one linear...

Hi everyone, I've finished the first week of my summer research internship, and I think I desperately need help. I very naively had thought I had "mastered" the art of learning after repeatedly raking in high marks in my courses, but now I feel like I'm completely out of my league and...

Question in the title, ie why is Tr(T_{a_1}T_{a_2}...T_{a_n}) independent of which representation we choose, where the Ts are a matrix representation of the group generators.

[b]1. A fair coin is tossed n times, let E be the event that the first toss is a head and Fk be the event that there are a total of k heads. For which values of n, k are E and fk independent events? [b]3. I don't see how these events can possibly be independent (surely the first influences...

I had an interesting conversation today with one of the senior professors in my department. It was in the context of students who have some difficulty in defining a project. What came into question was the level of independence of Ph.D. students should display with respect to their research...

Hi, I am a little confused how do you find out when a matrix has two independent eigenvectors or when it has one or when it has more than two, or is it possible it can have no eigenvectors.

[b]1. State the one dimensional time - INdependant Schrodinger equation for a particle of mass m and total energy E in a potential V(x). For an infinite square potential well V(x)=0 (0<x<l) and V(x) = infinite (all other x) find a general solutionfor the wavefunction of this function of this...

Hey everyone, I'm working on my undergraduate thesis in biology and am having problems analyzing the data from my experiments. I'm wondering if anyone knows how to compare multiple independent groups when the measurements are proportions. The problem is that many of my values are 1 and 0 with...

So I am going through Serge Lang's Algebra and he left a proof as an exercise, and I simply can't figure it out... I was wondering if someone could point me in the right direction: If f is a polynomial in n-variables over a commutative ring A, then f is homogeneous of degree d if and only if...

Homework Statement Let X and Y be two independent random variables with distribution functions F and G, respectively. Find the distribution functions of max(X,Y) and min(X,Y). Homework Equations The Attempt at a Solution Can someone give me a jumping off point for this problem...

Homework Statement Let the join probability density function of ZX and Y be given by f(x,y)=\left\{\stackrel{2e^{-(x+2y)}\ \ \ \ \ if\ x\ \geq,\ \ \ y\ \geq\ 0}{0\ \ \ \ \ \ \ otherwise} Find E(X^{2}Y) Homework Equations I approached this problem using a theorem from the book that states...

Homework Statement Given: \mathbf{H}=V_0\begin{bmatrix} 1-\epsilon & 0 & 0\\ 0 & 1& \epsilon\\ 0 & \epsilon & 2 \end{bmatrix} \epsilon<<1 a) Find eigenvalues and eigenvectors of the unperturbed Hamiltonian (\epsilon=0) b) Solve for eigenvalues of the Perturbed Hamiltonian...

Hey everyone, I've been thinking about my summer, and I would like to do some sort of research. I applied for some REUs, but it doesn't look like I've gotten into any. However, I would still like to learn something this summer. I've taken DE, Linear Algebra, Abstract Algebra, and...

Assignment question: Let V = P (R) and for j >= 1 define T_j(f(x)) = f^j (x) where f^j(x) is the jth derivative of f(x). Prove that the set {T_1, T_2,..., T_n } is a linearly independent subset of L(V) for any positive integer n. I have no idea how...