Joint Definition and 327 Threads

A joint or articulation (or articular surface) is the connection made between bones in the body which link the skeletal system into a functional whole. They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally.

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  1. D

    Trying to design a robotic joint.

    Hi everyone. This is my first post on the forums. I wanted to ask your expertise on a project I'm working on. I'm trying to design a setup where I rotate a ∏ shaped frame that has a 1kg load on the horizontal bar. The space between the frame should stay empty. The length of the side rods...
  2. R

    Joint probability for an infinite number of random variables,

    Hi, I have the following question : How do we estimate the joint probability Pr(X_1, ... X_n) when n \rightarrow \infty ? Thanks a lot.
  3. W

    Joint hipergeometric and binomial probability?

    Have an example: 123455 111555 the sample space is 0..9 row 1 can pick 6 numbers out of which 2 are repeated row 2 can pick 6 numbers out of which 3 by 3 are repeated I want to know what is the real probability that row 1 will match with 2 distinct numbers numbers row 2, and a repeated number...
  4. O

    Joint PMF of x and y: Calculating c, Marginal PMFs, and Expected Values

    Homework Statement Hi, if you could offer help to any of these questions, it would be great, i was unable to attend my lectures this week and I had no idea how to do these. The joint pmf of x and y is p x,y = c(x^2 + y^2) x,y = 1,2,3 Find: a. c and the marginal pmfs of x and y b. e(x)...
  5. E

    Gaussian random variable joint density with discrete pdf

    Hi all, I am having trouble with the concept of joint pdf's. For example - a set Z1,Z2,...ZN are each gaussian rv. Let Z1~N(0,1), let X be +1 or -1 each with probability 0.5. Z2=Z1X1, so Z2 is ~N(0,1). (I assume this to be As Z2 is just Z1 multiplied by a simple factor, an instance...
  6. D

    Double Cardan Joint and angular velocity

    1. Homework Statement What is the angular speed of a driven shaft whent he drive shaft is 40.34774 RPM? Assume that the cardan joints are offset by 45 degrees or less. 2. Homework Equations Angular Velocity relationship w2/w1 = cos(d)/(1-sin^2(o2)*sin^2(d) w = angular velocity...
  7. S

    Joint distribution function of z and |z|

    X and Y are 2 independent gaussian random variables with parameter a. Z = XY / (X-Y) W = XY / |X-Y| I am to find the joint distribution function of z and w. I know how to find pdf of Z but how could I use it to find the joint distribution function of z and w?
  8. N

    Finding a probability given joint p.d.f of the continuous random variables

    I'm having a trouble doing this kind of problems :S Lets try this for example: The joint p.d.f of the continuous random variable X and Y is: f(x,y)= (2y+x)/8 for 0<x<2 ; 1<y<2 now we're asked to find a probability, say P(X+Y<2) I know i have to double integrate but how do I choose my...
  9. H

    Defective light bulbs - Joint probability

    Homework Statement Of 25 light bulbs, 5 are defective. 8 bulbs are chosen from the 25. What is the probability that 2 or fewer of the 8 selected light bulbs are defective? Homework Equations The Attempt at a Solution It's been awhile since I've done questions like this one. I was...
  10. B

    Find the joint with the best thermal conductivity ?

    Hi Experts I'm joining aluminium fins to an aluminium body as part of a heat exchanger project. There are a number of variables here and I would like to evaluate them to achieve the best results. The best (simplest ?) method I can come up with is to attach several groups of fins to a common...
  11. D

    Kinematics Question - Double Cardan Joint

    Kinematics Question -- Double Cardan Joint Homework Statement What is the angular speed of a driven shaft whent he drive shaft is 40.34774 RPM? Assume that the cardan joints are offset by 45 degrees or less. Homework Equations Angular Velocity relationship w2/w1 =...
  12. G

    How Do You Calculate Covariance from a Joint Probability Table?

    A bag contains three green beads, two red beads and a blue bead. You select two beads at random. Let G denote the number of green beads and R the number of red beads you select. (a) Write the joint probability distribution of (G,R) in a table. Show that Cov(G;R) < 0. I can do P(G=g)...
  13. Shackleford

    Joint Distribution of X & Y: Visualizing Relationships

    My answer is not really close to the answers provided. They break up the joint distribution into x less than y and y less/equal to x. They have a 1 in their cases. I don't. http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-1.png?t=1302832281...
  14. S

    Joint density functions (gaussian)

    Would just like a hand with this question If X and Y are independent standard Gaussian random variables (that is, independent N(0, 1) 's ) do the following: (a) Write down the joint probability density function fXX,Y (x, y) of X and Y . I know what the gaussian density function looks...
  15. Femme_physics

    In trusses, does the number of screws on a joint matter?

    we're going to start trusses soon (statics) and I want to know if I should pay attention to several screws on a joint...for instance, I attached a question and in the drawing I see sometimes 2 and sometimes 3 screws on a joint...is it relevant, or should I treat them as though they were one screw?
  16. Astronuc

    ATK, EADS Astrium Joint Development

    ATK, EADS Astrium To Develop Liberty Rocket. http://online.wsj.com/article/SB10001424052748704422204576130482887509152.html The team wants to build a low-cost commercial launcher (300 ft tall) to lift U.S. astronauts and scientific payloads into space. Looks similar to the proposed ARES...
  17. I

    Limits of Integration Re: Joint Probability Functions

    Edit: I'm not sure if this post was deleted by an admin or if I just didn't click on the submit button. Apologies in advance if it was the former, but I reposted since I couldn't think of a reason why this post would be deleted Homework Statement f(x,y)=24xy for 0<= x<=1, 0<=y<=1, 0<=x+y<=1...
  18. S

    Characteristic function of joint distribution

    What exactly is a "joint characteristic function"? I want the characteristic function of the joint distribution of two (non-independent) probability distributions. I'll state the problem below for clarity. So my two distributions are the normal distribution with mean 0 and variance n, and the...
  19. C

    True or False: Joint CDF Has Only One Global Max?

    True or false: "Every joint CDF has only one global maximum at F(x1*, ..., xn*) = 1? I know that the multivariate CDF is monotonically non-decreasing in each of its variables. But does that imply that it has only one global maximum? Is it possible to have two or more separate peaks where the...
  20. L

    What is the Joint Characteristic Function of Sn and Sm Given Their Covariance?

    1. The problem statement X1,X2,X3...Xn are RVs with the same mean and covariance function as follow : COV(Xi,Xj)=ρ (σ)^|i-j| if Sn=X1+X2+...Xm , Sm=X1+X2+...Xm where m<n find the joint characterisitic function of Sn and Sm 2. Homework Equations . the general equation of the...
  21. H

    Joint Density problem again: What am I doing wrong?

    Hello, I would gladly appreciate any and all help with this joint density problem a practice problem for an exam. Please excuse my lack of use of the proper symbols, I don't know how to express them online unfortunately : Joint Density of two random variables, U and V is: f(u,v)= 1/u...
  22. H

    Can someone check my work for this joint denisty function problem

    Homework Statement X and Y have uniform joint density function: f(x,y)= d (constant) for 0<x<1 and 0<y<1-x 1. find d 2. find p(y<x) 3. find cov (x,y)The Attempt at a Solution 1. For this I first graphed x=1 and y=1 and created a square since x can go from 0 to a maximum of 1 and y also. I...
  23. K

    Statistics - difference between joint distribution and joint density?

    Homework Statement This is just a general question about understanding. What is the difference between a joint distribution functions vs. a joint density function. Homework Equations The Attempt at a Solution Are joint density functions basically the joint distributions of...
  24. K

    Multiple Random Variables - find probability given joint pdf

    Homework Statement Show that the function defined by f(x,y,z,u) = 24*(1+x+y+z+u)^(-5) for x,y,z,u>0 and f=0 elsewhere is a joint density function. Find P(X>Y>Z>U) and P(X+Y+Z+U>=1). Homework Equations distribution function = quadruple integral from 0 to x (or y or z or u) here of the...
  25. L

    Solving Joint Distribution of Exponential RVs: X, Y, Z & U

    Hi , I got this question in my midterm today but up till now I don't know how to solve it , The Question is as follow : If X and Y are two exponential Rv with different lambda . and there's a new Rvs Z and U are defined such that : Z= 0 : X<Y and 1 : X=> Y U= min(X,Y) and the...
  26. T

    Stats: Joint Density/Independence - Method of transformation (please check)

    Homework Statement Let X_1 and X_2 be independent \text{Exp}(\lambda) random variables. (i) Find the joint density of Y_1 = X_1 + X_2 and \displaystyle Y_2 = \frac{X_1}{X_2} (ii) Show that Y_1 and Y_2 are independent. The Attempt at a Solution (i) By independence of X_1 and X_2...
  27. S

    Joint Density Probability Question

    Homework Statement I am having trouble understanding the results of a homework problem and want to make sure I'm doing it right. The problem states that the joint density f(x,y) is equal to 1 in the shaded area and 0 elsewhere. The graph for f(x,y) looks like the attachment. The problem...
  28. S

    Help with joint distributions?

    Homework Statement Suppose X and Y have joint density f(x,y)=2 for 0<y<x<1. Find P(X-Y>z) According to the textbook the answer should be (1-z)^{2}/2 Homework Equations The Attempt at a Solution \int \int 2dxdy for x=[0, z+y] and y=[0,1] =\int 2(z+y) dy =2z+1 since we...
  29. R

    Using joint probability mass functions

    I know assignment questions and such aren't meant to be placed in here, but there's no spot in the "homework section" that's meant for statistics. Move this to the appropriate section if necessary; I couldn't find it. Here I have an image of the questions we are meant to answer. The...
  30. K

    Probability - Getting joint distribution?

    Homework Statement I have 2 variables that are both i.i.d. X1 and X2. i.i.d means they both have the same distribution and are independent of each other. My question is, how do i get the joint distribution: Fx1,x2(x1,x2) of these variables?? Homework Equations The Attempt at a...
  31. H

    Joint Probability Density Function

    Homework Statement X and Y are random variables with the joint density: fXY(x,y) = k*e^(-lambda * x) if 0 < y < x < infinity = 0, otherwise Find P(X + 2*Y <= 3) Homework Equations I found k = lambda^2 The Attempt at a Solution I'm not sure exactly how to solve this, but...
  32. M

    Did I do this joint density problem correctly?

    Homework Statement 1. Calculate Fxy(.25,.25) 2. Calculate Fx(.25) 3. Calculate Fy(.25) Homework Equations f(xy) = 2 (x+y) if 0\leq x \leq 1 and 0 \leq y \leq x The Attempt at a Solution 1. without showing all of the steps of my integration (because I apparently can't work...
  33. C

    Understanding Joint PDF and Independence in Probability: Solving for P(X+Y<=2)

    Let the joint PDF of (X,Y) be of the form: f(x,y) = 1/8x(x-y), 0<=x<=2, |y|<=x f(x,y) = 0 elsewhere Find P(X+Y<=2). The answer that my teacher gave was P(X+Y<=2)=∫01dx ∫-xx 1/8x(x-y)dy + ∫12dx ∫-x2-x 1/8x(x-y)dy I do not understand how my teacher could separate the integral like...
  34. M

    Ball and socket joint FSI modelling

    Hello all, Just would like to some input from the engineering world on this. I would like to model the lubrication film between a ball and socket joint using FE/CFD co-simulations. In reality the ball and socket arrangement would be located in a bath of fluid and the fluid would provide...
  35. C

    Probability of a curve in joint density plane

    Suppose X and Y are continuous random variables with the joint pdf f_{xy}(x,y) on the [0,1] \times [0,1] square. Is the probability P(X = Y) then equal to zero since probability here is a volume, and the set that satisfies P(X = Y) is a plane? Supposing it's not zero, when I tried to evaluate...
  36. P

    Understanding Joint Probability Model

    Hello everyone, I am trying to understand a paper and am stuck at one place. The statement says something as follows: Say we have a, b, c and d which are random variables generated by some model. This leads to the following joint probability model: p(a, b, c, d) =...
  37. L

    Centrifugal force versus gravity (ball on a joint placed on rotating shaft)

    Homework Statement Basically, this is the problem. [PLAIN]http://img180.imageshack.us/img180/3598/physicsproblem.png It's related to some design research I'm doing regarding a centrifugal control valve. This is a type of valve that controls the fluid flow based on the centrifugal...
  38. D

    Joint expectation of two functions of a random variable

    Ok I am not sure if I should put this question in the homework category of here but it’s a problem from schaums outline and I know the solution to it but I don’t understand the solution 100% so maybe someone can explain this to me. Let X and Y be defined by: \begin{array}{l} X = \cos \theta...
  39. G

    Change of variable - joint p.d.f

    Homework Statement X and Y uniformly distributed on the disc: 1/pi, x^2+y^2 <=1 X=Rcos(theta), Y =Rsin(theta) 0<=R<=1, 0<=theta<=2pi Find the joint PDF of R,theta The Attempt at a Solution g(R,theta)=f(x,y)*abs(jacobian) The Jacobian is R The joint PDF is then simply R/pi = 1/pi (since...
  40. S

    Engineering Joint probability problem

    Homework Statement axial load in an interior column in a two-story building is a random variable Y described as the sum of the floor loads X1 and X2 the floor load each is a normally distributed random variable with a mean value of 90kn.m and a coefficient of variation of .20. The random...
  41. Math Is Hard

    Medical Broken blood vessel in finger joint

    Friday morning I was sitting at my desk when I felt this burning sensation in my left hand. Suddenly the middle joint of my index finger started swelling up and it was very painful. Then the middle joint turned purple and looked like it had been hit with a hammer. It's been two days now and...
  42. Z

    Joint Probability of Sum Normal

    Don't know there are anyone can help me out with this. This is just something I asking myself, not a homework I must say. Let's define X and Y are 2 standard normal random variables. And random variable Z=X+Y. For real number a, we know P(X>a), the probability of X is greater than the...
  43. S

    Statics Question regarding Joint type & Reactions

    When solving for reactions in a 2D diagram as seen below, how does each type of joint affect the summation of forces in the x & y components? My problem asks to find the summation of forces in the x & y components, and has a smooth pin connection in the left of the beam and roller on the right...
  44. M

    What is the temperature at the joint between the two rods?

    Homework Statement The thermal conductivity of aluminum is twice that of brass. Two rods, one of aluminum and the other of brass, are joined together end to end in excellent thermal contact. They are of equal lengths and radii. The free end of the brass rod is maintained at 0°C while...
  45. N

    Interesting Joint Stiffness Method

    So I was doing some FE work (w/ NASTRAN) to determine the stiffness in all 6 DOF of a model bolted to another model. To characterize the bolted interfaces I attached surface nodes within the bolt frustums to rigid body elements (RBE2). Then, these RBE2s were connected with a directional...
  46. S

    Relation of conditional and joint probability

    P(A|B)=\frac{P(B|A)P(A)}{P(B)} P(B|A)P(A)= \frac{(P(B)\cap (P(A)) P(A)}{P(A)}=P(B)\cap P(A)=P(A)\cap P(B) P(A|B)=\frac {(P(A)\cap P(B))\vee (P(B)\cap P(A))}{P(B)} 0\leq(P(A)\cap P(B))\leq P(A); P(A)\leq P(B) 0\leq(P(B)\cap P(A))\leq P(B); P(B)\leq P(A)
  47. K

    Joint probability density for independent continuous random variables

    Homework Statement X,Y,Z random variables. Let Y and Z be two independent continuous random variables with common probability density function f(x) =2exp(-2x); x > 0 0; x < 0 (i) Specify the joint probability density function of (Y;Z). (ii) Fix x > 0. Let h(y; z) = 1...
  48. Saladsamurai

    Joint Probability FunctionStatistical Independence

    Homework Statement Homework Equations If X and Y are statistically independent, then f(x,y) = g(x)h(y) where g(x) = \int f(x,y) dy h(y) = \int f(x,y) dx The Attempt at a Solution (a) g(x) = \int f(x,y) dy = \int_{y=0}^{1-x} 6x\, dy \Rightarrow g(x)=6x(1-x) and...
  49. F

    What is the Probability that Two Independent Coin Tossers Stop on the Same Toss?

    Problem: Suppose that the probability that a head appears when a coin is tossed is p and the probability that a tail occurs is q=1-p. Person A tosses the coin until the first head appears and stops. Person B does likewise. The results obtained by persons A and B are assumed to be independent...
  50. A

    What is the Joint Distribution Problem for Coupon Collection?

    Hello, I have a problem I need help with: Homework Statement There are 10 different types of coupons, each with prob 1/10 of being chosen. A total of N>=1 coupons are collected. Xi= 1 if type-i coupon is among the N coupons, i =1, ..., 10 0 otherwise Let S=X1+X2+X3 be the number of...
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