Multivariate Definition and 121 Threads

If the covariance matrix \mathbf{\Sigma} of the multivariate normal distribution is invertible one can derive the density function: f(x_1,...,x_n) = f(\mathbf{x}) =...

Title says it all. Examples from class I am looking at include: lim(x,y) -> (0,0) of functions such as: 6yx^3 / 2x^4 + y^4 or (x^2)(sin^2 (y)) / x^2 + 2y^2 My professor did a bad job of explaining it (or at least I did not understand). Thanks, Nkk

I am a Computer Science student who wants to implement the EM statistical clustering algorithm. I'm doing this on my spare time outside of any classes that I'm taking. I've been doing a lot of reading and understand almost everything I need to fully. However, I only understand univariable normal...

I was wondering if it were possible to efficiently solve the common root of 4 polynomials in 4 variables algebraically. I am currently using a gradient descent method, which can find these roots in a couple seconds; however, I am concerned about local minima. So far I have attempted to use...

Homework Statement My goal is to have enough info that I could sit down with a piece of paper and actually compute a pretend test from start to end. All the examples and docs I have found online are not nearly in layman's terms.. oh, please excuse my math-lameness btw. :-) If I have 5-7...

I would need to evaluate the integral \int\limits_{x\in S}[x+x_A]^TA[x+x_A]\exp\left(-\frac{1}{4}[x+x_B]^TB[x+x_B]\right)dx where x is a column n-vector x_A and x_B are column n-vector constants A and B are n\times n (symmetrical) matrices taken over the volume S, which is a n-simplex* in...

Homework Statement Show that: max{a,b}=1/2*(a+b+|a-b|) Hence or otherwise, show that if f,g:R ----> R are continuous, then the function h:R ----> R defined by h(x) = max{f(x),g(x)} is also continuos. Suppose the f:(0,inf) ---> R is differentiable and f(x) ---> 0 as x---> inf. Set...

Hi, could anyone tell me the steps to solve the following question: Find the solution of x'=Ax with the initial value -------1---------2 0 0 x(0)=( 0 ), if A=( 0 1 -1 ) -------1---------1 1 1

Homework Statement Z = (Z1, Z2, ... Zd) is a d-dimensional normal variable with distribution N(0, E). Let A be invertible matrix such that AA' = E. (E = sigma = covariance matrix). Find the distribution of Y = (A^-1)*Z. The Attempt at a Solution I'm pretty sure the solution is normal...

Homework Statement Let Y be the number of customers entering a ABC bank in a day. It is known that Y has a Poisson distribution with some unknown mean lambda. Suppose that 1% of the customers entering the branch in a day open a new ABC bank account. Find the mean and variance of the number of...

In my math class lectures at the university while studying multivariable functions the lecturer never mentioned L'hopital's rule for these multivariate functions..But in a tutorial class,a tutorial assistant approached this question..find lim (x,y)-->(0,0) [sin(x^2+y^2)]/(x^2+y^2)..by implicitly...

I am currently studying multivariate calculus, and quite frankly, I'm not doing well. I am currently using Thomas' Calculus, 11/e media upgrade by Pearson. I don't like this book. The text is 75% theory and 25% simple examples, too few exercise problems, and the explanation is just too difficult...

Homework Statement This is a second (university) year calculus problem dealing with calculus of multiple variables. In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of goods. A utility function u = u(a,b) gives the utility from consuming...

Homework Statement Calculate the taylor polynom of order 3 at (0,0,0) of the function with well-known series (that means I can't just take the derivatives) f(x,y,z)=\sqrt{e^{-x}+\sin y+z^{2}} Homework Equations The Attempt at a Solution I wrote the functions within the square...

[SOLVED] Multivariate Linear Regression With Coefficient Constraint I'm attempting a multivariate linear regression (mvlr) by method of least squares. Basically, I'm solving a matrix of the following form for \beta_p, $ \begin{bmatrix} \sum y \\ \sum x_1 y \\ \sum x_2 y \\ \sum x_3 y...

Hi to all :) Does anyone have any idea how the expression for a multivariate exponential distribution looks like? If possible, can you post the source url? Commonly available is the multivariate normal distribution. thanks in advance :biggrin:

Hi everyone I'm just about to begin a course in multivariate and vector calculus what prior knowledge in maths is good to go over to help me along the way in this course?

I have temperature data from two different sites, and I want to develop a relationship for temperature between those two sites. In that way, if I have temperature at just one of those sites, I can approximate the temperature at the other site. My question is whether or not a multivariate...

Working from "Principles of Mathematical Analysis", by Walter Rudin I have gleaned the following definition of continuity of a function (which maps a subset one metric space into another): Suppose f:E\rightarrow Y, where \left( X, d_{X}\right) \mbox{ and } \left( Y, d_{Y}\right) are metric...

here is the problem, and I can't seem to get very far, compute the length of r(t) = <3t, 4cost, 4sint> from t=0 to t=1 i know the formula is integral from 0 to 1 of length of r'(t) but I keep coming up with 5, and it doesn't seem right, can someone please confirm or deny this. Thanks

I'm stuck on this question Show that f(x1,x2) has a strict local minimizer at t=0 along every line { x1=at { x2=bt through (0,0). Any hints or tips would be great thanks