Joint Definition and 327 Threads

I have a region R = {(x,y): |x| + |y| <= 1} I have sketched the graph on the x-y plane and shaded in the region R (I got a diamond). How do I find the area of R and hence find the joint density function f(x,y) and how do I specify the region for which f(x,y) is non-zero.

Obtain marginal probability mass function (pmf) given joint pmf Not really a homework question, but it does have a homeworky flavor, doesn't it... Homework Statement Given a join probability mass function of two variables, is it always possible to obtain the marginals? E.g., if I have a...

Homework Statement f\left(x,y\right)=\left\{\begin{array}{cc}\frac{1}{y} ,&\mbox{ if } 0 \leq x \leq y, 0 \leq y \leq 1 \\ 0,&mbox{ otherwise } \end{array}\right. Find the marginal distributions (pdf and cdf) of X and Y Find Pr(X+Y>0.5) Homework Equations N/AThe Attempt at a Solution...

Homework Statement X1 and X2 represent the values of two honest dice throws (independent of each other). Find the joint probability function of U and V when: a) U = min{X1,X2}, V = X1 + X2 The Attempt at a Solution This is what I thought: P(U = u,V = v) = P(\min \left\{...

Homework Statement Given: f(x,y) = x + y, for 0<x<1 and 0<y<1 f(x,y) = 0, otherwise Derive the joint distribution function of X and Y. Homework Equations N.A. The Attempt at a Solution Using the definition, I obtained part of the joint distribution F(x,y) = (1/2)(xy)(x+y)...

Please explain in detail about toggle joint, especially about its mechanical advantage.

Homework Statement Two players, A and B, try to see who has the fastest reflects. They test this by using a button, and whoever presses the button first when a light goes on, wins. Let's assume both A and B are random variables ~U(0,1) and are independent (time in seconds). May W = "winner's...

Homework Statement John and George are set to meet each other at 12 o'clock. John's time of arrival, J, is distributed uniformly between 12:00 and 12:15. John will wait for George for 15 minutes. If he doesn't show up, he leaves. George's time of arrival, G, is also uniformly distributed...

Dear all I have the following problem. Given a set of correlated binary variables, can I determine the joint probability from the correlation function? {Xi} is a set of binary variables Pr(Xi=1) = p and Pr(Xi=0) = q for all i Corr(Xi Xj) = cij cij is symmetric Now how can I determine the...

Homework Statement Find the Corresponding normalization constants for the joint guassian \\p\\(x,y) \alpha\ exp(-(ax^2/2) - (by^2/2) -cxy) ie: find P(x), P(y), and P(X,Y) normalization constants relevant equations: Mutual Information: M(x,y) \\M(x,y) =...

http://s44.photobucket.com/albums/f46/maximus11373/?action=view&current=w-1.jpg&newest=1 An inclined member is braced with a glued block, as shown. The ultimate shear stress in the glued joint is 1050 psi. Determine the dimension X at which the glued joint will fail. I know that...

For a rivet joint under eccentric loading, there exist a primary shear stress and an additional shear stress due to the eccentric load giving a moment about the centroid of the rivet joint. The formula to calculate the force giving the additional shear stress is... Fi=P x e x ri/...

Homework Statement Let Y= X1 + X2 and Y2 = X2 + X3 where X1 X2 and X3 are three independent random variables. Find the joint mgf and the correlation coefficient of Y1 and Y2 provided that a) Xi has a Poisson distribution with mean mi i = 1, 2, 3 b) Xi is N(mi, si2) i = 1, 2, 3 The...

if the joint p.d.f of x,y is given by f(x,y)= a |x-y| ,0<=x,y<=1 f(x,y)= 0 , o.w find i)a ii)p(y>x) iii)p(x=y)

Homework Statement Stuck on this for quite some time. http://img685.imageshack.us/img685/1387/22580211.png Homework Equations The Attempt at a Solution I've drawn the component parts in question. Don't know where to even begin to find this solution (dont have my scanner here too). I am...

I'm a science freshman (U0) at McGill and I can't seem to find the answer to this question on any website. I've sent it by email to my advisor, but have not got a response back yet. My question to anyone that goes or has gone to McGill is: What exactly are the requirements for entry into the...

Are any two (or n) random variables always jointly distributed in some sense? When will two RV's be non jointly distributed? Saurav

Homework Statement Let X1 X2 X3 be independent and identically distributed random variables with common pdf f(x) = e^-x 0<x<infinity, zero elsewhere. Evaluate P(X1 < X2|X1 < 2X2) and P(X1 < X2 < X3|X3 < 1). The Attempt at a Solution Would appreciate any hints as to where to start...

Homework Statement X1 and X2 are independent~u(0,1) Y1=X1+X2 Y2=X1-X2 Find the density function of Y1 Homework Equations X1=(Y1+Y2)/2 X2=(Y1-Y2)/2 0\leqY1\leq2 -1\leqY2\leq1 0\leqY1+Y2\leq2 0\leqY1-Y2\leq2 -y1\leqy2\leq2-y1 -1\leqy2\leqy1 The Attempt at a...

Homework Statement Let X and Y be independent uniform (0,1) random variables. a. find th ejoint density of U=X, V=X+Y. b. compute the density funciton of V. Homework Equations The Attempt at a Solution Part a. is not a problem. I don't understand how the bounds for part b...

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...

Homework Statement In a square town that is 1.5 miles by 1.5 miles, the places of residence are uniformly distributed (2000 per square mile) over the whole town. Compute the joint probability density function for the spatial distribution of places of residence (fX, Y). Homework Equations...

Evening everyone, i have been referring to Shigleys "Mechanical engineering design" (pages 349 to 351) regarding a welded joint I am looking at. wanted to compare my manual calcs to sum FEA. My joint is a circular shaft which is fillet welded to a base plate. A load is applied to the end...

hello i have given this problem to find pdf of function z.i have solved most of it and stuck at the end. i have attached problem and my solution so far as pdf here. what i want to know what are the integral limits for finding f(z) using marginal density (see the end the end of attached...

Homework Statement Homework Equations Well i know the double integral formula for the joint pdf The Attempt at a Solution So firstly we're told to find the joint pdf of X and Y. I'm not sure where to begin. So how do we find the function that we take the double integral over? I'm...

Homework Statement If and where X,Y are independent and identically distributed (i.i.d) random variables uniformly distributed over the interval (0,2). Z=X-Y W=X+Y (a) Find the joint pdf of Z and W . (b) Show that even though the random variables Z,W are uncorrelated they are not...

Homework Statement A dancer stands on his left leg (knee extended), torso and arms forwards outstretched horizontally. The right leg (knee extended) is backwards outstretched horizontally. The dancer weighs 55 kg. The length of the thigh is 35 cm, the shank 45 cm. Draw the free body diagram...

Homework Statement Let X and Y be two random variables, with joint distribution given by the following table: a b 1 2 3 4 -------------------------------------- 1 16/136 3/136 2/136 13/136 2 5/136 10/136 11/136 8/136 3...

For vectors we can define the Joint Guasian as follows: f_X(x_1, \dots, x_N) = \frac {1} {(2\pi)^{N/2}|\Sigma|^{1/2}} \exp \left( -\frac{1}{2} ( x - \mu)^\top \Sigma^{-1} (x - \mu) \right) Now what if (x - \mu) is a matrix A and \Sigma is an order four covariance matrix Q between ellements...

If A and B are two events and I want to look at their joint probability P(A.B) do I have to be concerned with the order in with A and B occur? Saurav

fx,y = 6(x-y)dydx, if 0<y<x<1 how do you find E(XY), i know the formula...g(x,y)fxy(x,y)dydx but i don't know what 'g(x,y)' represents and the limits to use??

Joint PDF --> Marginal Pdf's Homework Statement Suppose that the random vector (X, Y ) has the probability density function (pdf) fX,Y (x, y) = k(x − y), if 0 < y < x < 1 0, otherwise. 1. Find the value of k, so that fX,Y (x, y) is a genuine pdf. 2. Find the marginal...

Homework Statement Basically, I am looking to find the reaction forces at the pin joint on the right side of the structure. I just realized it is not labeled on my diagram, but it is the pin on the link opposite of E. Where the 13 degree angle is measured from. Homework Equations I have...

This is a problem given for laboratory analysis, but there are no relevant equations in our textbook to help solving the problem. Could anyone just give me a hint on what equation should be used to solve the problem? the only relevant equation I know is : shear stress = F/A 1. The figure...

I read two articles recently and I am wondering if I have the correct interpretation of them. They deal with joint weak measurement and Hardy's paradox. Is the result of the "Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair" paper indicating...

Suppose that h is the probability density function of a continuous random variable. Let the joint probability density function of X, Y, and Z be f(x,y,z) = h(x)h(y)h(z) , x,y,zER Prove that P(X<Y<Z)=1/6 I don't know how to do this at all. This is suppose to be review since this is a...

Assume that two random variables (X,Y) are uniformly distributed on a circle with radius a. Then the joint probability density function is f(x,y) = \frac{1}{\pi a^2}, x^2 + y^2 <= a^2 f(x,y) = 0, otherwise Find the expected value of X. E(X) = \int^{\infty}_{- \infty}\int^{\infty}_{-...

Let X, Y, and Z have the joint probability density function f(x, y, z) = kx(y^2)z, for x>0, y<1, 0<z<2 find k \int_{0}^{2}\int_{- \infty}^{1}\int_{0}^{\infty}kxy^2z dx dy dz This integral should equal 1. Is my procedure correct so far? I don't manage to solve the integral...

If f(x,y) = 4xy, for 0<x<1, 0<y<1 f(x,y) = 0, elsewhere What's the probability that X<Y? It seems likely that the probability is 0.5, but how can I show it matematically?

Homework Statement A framework of pin jointed members has to be designed to support a plug introduced into the reservoir wall to prevent leakage and further progression of a crack along the wall. The plug is cylindrical, has a diameter of 0.35 m and is supported by a single pin joint. The...

Homework Statement I have a square beam with a screwed joint at each end. I am trying to determine deflection under a uniformly distributed load. Homework Equations - What is a simplified form for the screwed joint? Is it to be assumed fixed at both ends? The Attempt at a...

Could anyone help to give an example where in the same proba space, x and y have each the density function, while the joint density function does not exist? Thanks in advance, Best regards

Hi, I am a quantum physicist who needs a practical help from mathematicians. :smile: The physical problem that I have can be reduced to the following mathematical problem: Assume that we have two correlated variables a and b. Assume that we know all conditional probabilities P(a|b), P(b|a)...

Homework Statement Calculate the knee joint angle based on the XY coordinates of the hip, knee and ankle joint centres. Hip joint(x = 1.0183, y = 0.7959) Knee joint(x = 1.1223, y = 0.5042) Ankle joint(x = 1.0539, y = 0.1081) Homework Equations θjoint = θproximal −θdistal The...

An aluminum wire of length .6 m, cross sectional area of .01 cm^2, density 2.60 g/cm^3, is tied to a steel wire of density 7.8 g/cm^3 and the same cross sectional area. The compound wire is joined to a pulley and then a block of mass 10 kg is tied at the end of the steel wire. Thisi is...

Homework Statement The following table gives the joint probability mass function (p.m.f) of the random variables X and Y. http://img170.imageshack.us/img170/555/tableph9.jpg Find the marginal p.m.f's P_X \left( x \right) and P_Y \left( y \right) 2. The attempt at a solution I think I have...

Homework Statement Let X1, X2, X3,...Xn be independent and indentically distributed with pdf f_X(x)= 4x^3 for 0 < x < 1 First I had to calculate the joint pdf of distribution of X1, X2, X3..Xn which I did I got 4(X1*X2*X3*...*Xn)^3 Which I'm hoping is correct. a) determine the...

Homework Statement Consider two components and three types of shocks. A type 1 shock causes component 1 to fail, a type 2 shock causes component 2 to fail, and a type 3 shock causes both components 1 and 2 to fail. The times until shocks 1, 2, and 3 occur are independent exponential random...

I have a general question about solving these types of problems. I had two different problems for calculating the tensions and compressions of a pin-jointed truss. both problems were of a trapezoidal shape with 5 pins in total. in one problem, a weight was applied to the center truss on...

Homework Statement Consider a rod length L and mass m which is pivoted at one end. An object with mass m attached to the free end of the rod. g=9.8 m/s^2. Note: Contrary to the diagram shown, consider the mass at the end of the rod to be a point particle. Basically it looks like a rod...