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. stripes

    Finding the joint moment generating function given the joint PDF

    Homework Statement Homework Equations The Attempt at a Solution The problem is the integral is non-elementary, so now what? Part (b) follows trivially from part (a). But is there some kind of shortcut I have to take, because no matter what substitution I do, the integral...
  2. atyy

    Joint distribution of position and momentum

    In quantum mechanics, there doesn't seem to be a joint distribution of position and momentum. But in Bohmian mechanics there is. But Bohmian mechanics is quantum mechanics, so what is the error in my reasoning?
  3. marellasunny

    Kinematic analysis:Application of defining path of joint

    I understand that defining the path of a joint in a mechanism comes under the category of 'kinematic analysis'. I do not understand why engineers do this,when all they need to know is the path of the piston,piston velocity and piston acceleration(kinematic analysis). Take for example this 90...
  4. G

    Joint Number state switching operator?

    Hi, I was just wondering if anyone know of an operator, which has some realistic analogue, that would perform the following action: A|N,0> = A|0,N> Where the ket's represent two joint fock states (i.e. two joint cavities) and A is the opeator I desire. I thought that the beam...
  5. P

    Calculating Bolt Selection for Butt Joint Connections

    I am trying to select a bolt for a butt joint connection. When you guys do bolt selection, are there certain equations you use to determine if the bolt will rigidly hold the 2 parts together in the joint?
  6. K

    Average shear stress in the glue joint between a spliced rod?

    Problem statement: Two 3/4-in.-diameter nylon rods are spliced together by gluing a 2-in. section of plastic pipe over the rod ends, as shown in the figure. If a tensile force of P = 500 lb is applied to the spliced nylon rod, what is the average shear stress in the glue going between the pipe...
  7. schrodingerscat11

    Getting the joint probability density for the characteristic equation

    Dear all, Greetings! I was given a problem from Reichl's Statistical Physics book. Thank you very much for taking time to read my post. Homework Statement The stochastic variables X and Y are independent and Gaussian distributed with first moment <x> = <y> = 0 and standard deviation...
  8. schrodingerscat11

    Getting the joint probability density for the characteristic equation

    Homework Statement The stochastic variables X and Y are independent and Gaussian distributed with first moment <x> = <y> = 0 and standard deviation σx = σy = 1. Find the characteristic function for the random variable Z = X2+Y2, and compute the moments <z>, <z2> and <z3>. Find the first 3...
  9. N

    Why Is Joint IH Classified as Tension?

    Homework Statement Determine whether each joint is in tension or compression (correct answers on the image) Homework Equations sum of force = 0 The Attempt at a Solution On Joint I, I don't understand why IH is in tension. The pin is exerting a horizontal force and...
  10. O

    MHB Joint cumulative distribution of dependent variables

    Hello everyone! The problem: $X,Y,Z$ are random variables that are dependent and uniformly-distributed in $[0,1]$, and let $\alpha$ be a given number in $[0,1]$. I am asked to compute the following: $\text{Pr}(X+Y+Z>\alpha \;\;\; \& \;\;\; X+Y\leq \alpha)$ What I have so far...
  11. N

    MHB Unlock the Mystery of Tricky Joint PDF with Expert Tips | Attached Image

    Please refer to the attached image. How am I supposed to integrate this, it's impossible to find anything!
  12. N

    MHB Conditional expectation of joint PMF

    (please refer to attached image) The question appears to be simple enough, but i have two queries A) does E[X1 X2] mean the same as E[X1 | X2] B) If not/so, how exactly do I go about computing this. I've seen a few formulas in my lectures notes for computing conditional expectations for...
  13. J

    Joint PMF of Rolling a 6-Sided Die 5 Times

    Homework Statement Roll a 6-sided die 5 times. Event X is when a 1,2,3 shows up. Event Y is when 4,5 show up. Show the joint PMF. Homework Equations The Attempt at a Solution So... here is where I am at... X~Bin(5,0.5) & Y~Bin(5,1/3) P(X=x)=(5 C x)(.5^5) &...
  14. C

    Expectation of a Joint Distribution

    The below gives all the information I was given. I'm pretty sure my answer is right, but a part of me isn't, and that's why I'm asking here. Homework Statement Let (X,Y) have the joint pdf: f_{XY}(x,y)=e^{-y}, 0 < x < y < \infty Find E(XY). Homework Equations...
  15. S

    Solving a Pin Joint System with Vertical Load

    Hi all,I just started to learn mechanics so please forgive me if i ask something elementary.I have an example from Egor P Popov's Engineering mechanics of solids.(Please refer attachment and sorry about quality of drawing). This is a problem of a pin joint system subjected to vertical load...
  16. P

    Find marginal pdf given joint pdf (stats)

    Homework Statement Given joint pdf: f(x,y) = (2/(x2(x-1)))(y-(2x-1)/(x-1)) x>1, y>1 find marginal pdf fx(x) Homework Equations fx(x) = ∫f(x,y)dy, 0, ∞ The Attempt at a Solution fx(x) = ∫(2/(x2(x-1)))(y-(2x-1)/(x-1)) dy, 1, ∞ = [-2y(x/(1-x))/x3],1,∞ = undefined. stuck here
  17. A

    Programs A joint major in Computer Science and Engineering

    Hello, I'm about to be a Sophomore in Fall this year and current major is Software Engineering. My school offers a joint major in Computer Science and Engineering (as well as separate CS and Comp. Engr.). I'm looking into it as I don't want to be pigeon-holed as just a programmer but I'm not...
  18. O

    MHB How to Determine the Joint Distribution of X+Y and X-Y?

    Suppose u1 and U2 are a sample from Unif(0,1). X= 1{u1<=1/2} , Y=1{u2<=1/3} Get the joint dist of X+Y and X-Y Is it jointly discrete or jointly abs cont? How do info about finding the joint dist??
  19. C

    Compressive/Tensive Force at joint

    If "A" were a joint of the body, what is the compressive/tensive force at the joint? I already figured out the torque about A to be 6.840 Nm, but I'm not quite sure how to go about figuring out compressive/tensive forces. Normally, there would be a force associated in the area or angles...
  20. P

    Statistics - joint and marginal densities.

    Hi, Homework Statement I am having difficulties understand parts of the solution to the following problem in Statistics: Let X and Y be two random, continuous variables, where X is distributed U(0,1) and Y|X=x is distributed U(x,x+1). I am asked to find the marginal density of Y. Homework...
  21. M

    Joint Probability density function

    A joint pdf is given as pxy(x,y)=(1/4)^2 exp[-1/2 (|x| + |y|)] for x and y between minus and plus infinity. Find the joint pdf W=XY and Z=Y/X. f(w,z)=∫∫f(x,y)=∫∫(1/4)^2*e^(-(|x|+|y|)/2)dxdy -∞<x,y<∞ Someone told me I can not use Jacobian because of the absolute value. Is that true? So...
  22. E

    Question about truss joint analysis in ansys workbench

    Dear Friends, Hi,I am senior mechanical engineering student and I'm working on my final project which is designing an AGV vehicle.I designed a space chassis for it and have a problem with analyzing the joint I designed using Solidworks.I do not know how can I should define support...
  23. M

    LaPlacian joint probability density function.

    A joint pdf is given as pxy(x,y)=(1/4)^2 exp[-1/2 (|x| + |y|)] for x and y between minus and plus infinity. Find the joint pdf W=XY and Z=Y/X. f(w,z)=∫∫f(x,y)=∫∫(1/4)^2*e^(-(|x|+|y|)/2)dxdy -∞<x,y<∞ Someone told me I can not use Jacobian because of the absolute value. Is that true? So far this...
  24. M

    What is the joint pdf for W=XY and Z=Y/X in the LaPlacian distribution?

    A joint pdf is given as pxy(x,y)=(1/4)^2 exp[-1/2 (|x| + |y|)] for x and y between minus and plus infinity. Find the joint pdf W=XY and Z=Y/X. f(w,z)=∫∫f(x,y)=∫∫(1/4)^2*e^(-(|x|+|y|)/2)dxdy -∞<x,y<∞ Someone told me I can not use Jacobian because of the absolute value. Is that true...
  25. G

    Joint probability distribution

    Homework Statement f(x,y) = x2 + xy3 for 0 < x < 1, 0 < y < 2 and 0 otherwise. Calculate P(X+Y < 1) Homework Equations The Attempt at a Solution P(X+Y < 1) = P(X < 1-Y) which means y is now bounded by 0:1 instead of 0:2 and x is bounded by 0:y. So we get ∫[0-1]∫[0-y] x2 +...
  26. B

    Statistics - Joint PMF / Hypothesis Testing

    Homework Statement We sample a population 50 times with replacement, with all individual sampled equally likely. We survey the gender and quality of life. The counts are: Male: 13 high quality, 11 low | female: 18 high, 8 low. Let P_M, P_F, P_H, P_L to denote these population proportions for...
  27. D

    Joint probability density function

    I'm practicing the past year papers to prepare for my coming finals. Please make necessary corrections if you feel something wrong with it, thanks! Also, I'm supposed to do this in less than half an hour, so any suggestions on how to shorten this answer is really much appreciated! Homework...
  28. X

    Joint Major (with Nuclear Engineering)

    Hello everyone, I am a high school senior. I got accepted to UC Berkeley, and will be attending the school this coming fall. I want to pursue nuclear engineering in college. Since UC Berkeley offers joint major programs, I would like to pursue a joint major (nuclear + another engineering...
  29. S

    Joint, Continuous Random Variables Question

    Homework Statement Let X and Y have the joint probability density function f(x,y)=k(1-y), if 0<x<y<1 and 0 elsewhere. a)Find the value of k that makes this pdf valid. b) Find P(X<3/4,Y>1/2) c) Find the marginal density function of X and Y d) Find the expected value and variance of X and...
  30. P

    How Do You Calculate P(X>4Y) with the Given Joint PDF?

    Homework Statement Suppose X and Y have the joint probability density function: f(x,y) = x+4y, 0<y<x<1 f(x,y) = 0 otherwise Find P(X>4Y) Homework Equations The Attempt at a Solution I'm not sure how to do this. I've already found marginal pdf's for x and y.. although I...
  31. E

    Joint PDF of two continuous random variables

    Homework Statement The joint PDF (probability density function) ##p_{X,Y}(x,y)## of two continuous random variables by: $$ p_{X,Y}= Axy e^{-(x^2)}e^{\frac{-y^2}{2}}u(x)u(y)$$ a) find A b) Find ##p_X (x), \ p_{y}, \ p_{X|Y}(x|y), and \ p_{Y|X}(y|x)## Homework Equations The first...
  32. P

    What is the Marginal PDF of X?

    Homework Statement Let X and Y be random variables of the continuous type having the join p.d.f.: f(x,y) = 8xy, 0<=x<=y<=1 Find the marginal pdf's of X. Write your answer in terms of x. Find the marginal pdf's of X. Write your answer in terms of x. Homework Equations The...
  33. E

    HAT - Displacement of joint of the rods

    Two rods of different materials with coefficients of linear expansion α1 and α2 respectively; Young's moduli Y1 & Y2 respectively; of initial lengths l1 and l2 respectively are joined at one end. the free ends are fixed to two vertical walls as shown in the fig. Temperature of the surrounding...
  34. C

    MHB Joint Probability Distributions

    I have this question: and I'm a little confused. To calculate joint distributions in the earlier questions i was using:P_{(\xi1,\xi2)}(x1,x2)=P_{(\xi1)}(x1)P_{(\xi2)}(x2)But that would mean that if:P_{(\xi1,\xi2)}(2,0)=0\ either\ P_{(\xi1)}(2)=0\ or\ P_{(\xi2)}(0)=0which can't be true in...
  35. twoski

    Joint Probability Density Function

    Homework Statement The joint probability density function of X and Y is given by f(x, y) = c( x3 + xy/4 )  0 < x < 1 0 < y < 2 (a) For what value of c is this a joint density function? (b) Using this value of c, compute the density function of Y . (c) Using this value of c, nd PfX...
  36. H

    Is a joint BS/MS in Mathematics worth considering?

    As I've been looking at universities this year, a lot of them offer a joint bachelors and masters in math for undergrads, and I'm unsure if this is a good idea. I'm afraid that I won't get a thorough, well-rounded education if I rush through things, but on the other hand it could be helpful get...
  37. E

    Show that x and y are independent in this joint distribution

    Given that the joint probability Pr(w,x,y,z) over four variables factorizes as Pr(w,x,y,z) = Pr(w) Pr(z|y) Pr(y|x,w)Pr(x) show that x is independent of w by showing that Pr(x,w) = Pr(x)Pr(w). Attempt: if we simply assume Pr(x,w) = Pr(x)Pr(w), then: \begin{align} Pr(w,x,y,z) &= Pr(w)...
  38. F

    Impedance matching joint between cable and ground

    I would like to impedance match a few joints in a circuit and would appreciate some thoughts about this, since I would like the match to be as perfect as possible. The problem is complicated by the fact that the available equipment only consists of trimpot(s). The joints are mostly cables to...
  39. M

    Calculating Density Function of Joint Independent Exponential Random Variables

    X and Y are independent, exponentially distributed random variables - with possibly different parameters Determine the density func. of Z = X / Y How to attack ?
  40. M

    Bayesian computation of joint density, marginal posterior

    Homework Statement Hi, so I am having trouble understanding the steps to get to certain densities. For example, suppose i have data y1,...,yJ ~ Binomial (nj,θj) We also have that θj ~ Beta (α,β) Now our joint posterior is: p(β,α,θ|y) ~ p(α,β) ∏ (\Gamma(α+β) / \Gamma(α)\Gamma(β))...
  41. J

    Obtaining marginal PDFs from joint PDF

    Homework Statement Hi all, I'm looking at the joint pdf F(x,y) = (8+xy^3)/64) for -1<x<1 and -2<y<2 (A plot of it is here: https://www.wolframalpha.com/input/?i=%288%2Bxy%5E3%29%2F64+x+from+-1+to+1%2C+y+from+-2+to+2 ...sorry about the ugly url) and trying to find the marginal PDFs for X and...
  42. J

    Marginal PDF for Uniformly Distributed X and Y?

    Hi all, I'm looking at the joint pdf F(x,y) = (8+xy^3)/64) for -1<x<1 and -2<y<2 (A plot of it is here: https://www.wolframalpha.com/input/?i=%288%2Bxy%5E3%29%2F64+x+from+-1+to+1%2C+y+from+-2+to+2 ...sorry about the ugly url) and trying to find the marginal PDFs for X and Y. I know I want to...
  43. H

    Constant velocity joints vs. universal joint.

    i have to design an actuation system which will change the angle with which the power is transmitted through a motor,the range of angle is about,--35 to +35,w.r.t to the vertical,what should i use,a u joint or a velocity joint?there is a predefined load on the shaft(bending + torsional),what...
  44. S

    Joint PDFs and Expected Values of 3 Cont Rand Vars

    You know how sometimes, you take a long time to write a question, and then you submit, but it takes you to a login screen and then you lose everything you wrote? Anyhow...I would just like to verify some work here. The problems states that there are 3 mutually independent random variables...
  45. C

    Determine Joint Density & E[z] of f_xy(x,y) Function

    Homework Statement f_xy(x,y)= 24xy for o<x<1 and 0<y<1-x let z=[1-x]/y and w=y determine joint density of wz and E(z) Homework Equations The Attempt at a Solution E[z] = Integral [0,1] integral [0,1-x] 24xy*(1-x)/y dydx = 2 The joint distribution doing a...
  46. M

    Expected value of joint distribution

    Homework Statement Suppose that f_{X,Y}(x,y)=\lambda^2e^{-\lambda(x+y)},0\le x,0\le y find E[X+Y]Homework Equations The Attempt at a Solution I just want to double check I didn't make a mistake: E[X+Y]=E[X]+E[Y]=\int_0^{\infty} x{\lambda} e^{-\lambda x} dx + \int_0^{\infty} y{\lambda}...
  47. G

    What is the process for designing a bolt joint for a static assembly?

    I have to calculate the number of M6 Button head screws required to hold a door panel of 40 kg when 700N (calculate at the center line of the mounting holes) of force is applied laterally. I want to consider only lateral case when the force is applied perpendicular to the door panel. Any idea...
  48. F

    Programs Is it beneficial to have joint advisors in a PhD program?

    I'm curious if anyone has any experience working for two advisers, particularly in two different fields. In my case, I'd focus on synthesizing materials in a chem lab (that focuses on synthesis) and then working in a EE/physics lab that would focus on characterizing said material, in particular...
  49. L

    Joint conditional probability in bayes net

    Homework Statement We are given a belief network such that the overall joint probability after accounting for conditional independence is: P(a,b,c,d,e) = P(a)P(c|a,b)P(d|b)P(e|d,b) The values provided are: P(a = false) = .02 P(b = false) = .95 P(c= false|a=true, b=true) = .97 P(c=...
  50. I

    Find the joint distribution of 2 R.V defined on a triangular support

    Find the joint CDF of 2 R.V with joint PDF of triangular support Homework Statement Given the 2 random variables X and Y, their joint density given by: f(x,y) = c(x + y^2) for all (x,y) in the triangle 0<y<x<1 and f(x,y) = 0 elsewhere. Compute the joint distribution function F(X,Y)...
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