1. A

    Joint probability of dependent variables

    I have multiple-input-muliple-output (MIMO) problem formulated as T(t) = N*(W(t) - F(t) ) F(t) = K*∑_i{ W_i(t) } that I need help in finding which math tools to apply. NOTE! I have very little experience with the type of statistical tools that I'm looking for, so be patient in how the...
  2. D

    Tree Diagram and Dependent probability.

    Hi so I need some help with this question? Following a survey, it is found that a train service in Japan is late 2% of the time. For a particular working week of 5 days, a passenger wishes to investigate the potential lateness of the train service. a) Find the probability that the train is...
  3. S

    Getting the dependent variable

    I've got this equation: 5000=500/(1 - c) Intuitively, I know that it is the same as 1 - c = 500/5000 but how do I show the working that shifts the 1 - c to the left? Thanks, Simon
  4. C

    Dependent / independent events

    Hi, I need to give a 5 minutes presentation on the following: “But WHY do I need to learn about dependent / independent events in probability? I’ll never use it once I leave school!” Probability and stats is not as strong as my pure maths skills but can anybody help to give some...
  5. A

    Linearly independent or dependent? HELP!

    Consider the following elements of the vector space of all functions from R to R: f(x) = 2^x+1, g(x) = 2^x−1, h(x) = 4^x Is the set {f, g, h} linearly independent or linearly dependent? Justify your answer.
  6. R

    Expected value of (x-y)^2 (x,y are dependent)

    Say I have two variables x and y, both belong to N~(0,1), but are dependent. E(x)=0, E(y)=0, Cov(x,y)=0.5 (therefore E(x*y)=0.5 in this case) If z=x-y, the expected value of z^2 is: E(z^2)=E((x-y)^2)=E(x^2-2xy+y^2)=E(x^2)+E(y^2)-2E(x*y)=-2E(x*y) Since E(x*y) is a positive number...
  7. M

    Can a variable be both Independent and Dependent (Troubles with the Chain Rule)

    According to Keisler's Elementary Calculus: an infinitesimal approach Chapter 2 / Section 2.6 / Pages 88-92 ( ) We have two cases for the Chain Rule, which are: (page 89) Case 1: dy / dt = dy / dx * dx / dt where X is independent in...
  8. A

    Find determinant and linearly dependent

    hello all . I have Question about the determinant and linearly dependent and it's : Let : a) Find det(B) in terms of k; b) For what value(s) of k are the column vectors of B linearly dependent; c) For k = 0, find det(B) and . can some one help me in this question and...
  9. O

    sets and dependent probability

    I have a simple question about sample space, sets, and dependent probability. Let's say you have a bag with 3 marbles, two green and one blue, so that your bag looks like this: G1, G2, B next we choose a marble from this bag, the probabilities for choosing a green marble vs a blue are...
  10. G

    The points are Z-linearly dependent

    If $E/\mathbb{Q}$ the elliptic curve $y^2=x^3+x^2-25x+29$ and $$P_1=\left (\frac{61}{4}, \frac{-469}{8}\right ), P_2=\left ( \frac{-335}{81}, \frac{-6868}{729}\right ) , P_3=\left ( 21, 96\right )$$ I have to show that these points are $\mathbb{Z}-$linearly dependent and indeed that...
  11. R

    Binomial distribution with dependent trials?

    I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, that slides over that string. For the given parameters p,k and n one must must determine the mean...
  12. B

    Time dependent Spectral Analysis

    Hi, i have a little problem in determining the Priestley's evolutionary spectra: I ve attached some formula that will be familiar to whom knows the argoument. I am not sure about the last formula in the photo, about the spectral density function. Can anybody tell me if it s right what i wrote...
  13. C

    Linearly dependent family

    Hi everyone ! :D I've got a mixed geometry/algebra problem Here it is : I've got a line D which is the intersection of two plane \left\{ \begin{array}{rcr} \phi_1(X)+d_1 & = & 0 \\ \phi_2(X)+d_2 & = & 0 \\ \end{array} \right. and a plane P : \phi_3(X)+d_3=0 with...
  14. H

    Is this linearly independent or dependent?

    Hi, nice forum :) I have the set {(0,1,1),(1,0,1)(-1,1,0)} is this a linearly independent or dependent set?
  15. 1

    linear independent or dependent set of functions

    hi guys I know this question probably has been asked before, if any one knows where the answer lies please point me there, else if i have a set of functions cos^2 x sin^2 x sec^2 and tan^2 x, I need to show that they are linearly dependent becuase one can be a linear combination of the...
  16. W

    Independent or Dependent

    Determine whether the samples are independent or dependent. A data set includes the morning and evening temperature for the last 210 days. Choose the correct answer below. a. The samples are dependent because there is not a natural pairing between the two samples. b. The samples are...
  17. A

    path dependent function with a definite path

    This question is about if I have a path dependent function but a deinite path, then can I take partial derivatives? And are the points that are along path A connected to the points that are along path B. If I consider a non-conservative vector field \vec{dt}= \frac{\vec{ds}}{V(z)}\ I must...
  18. V

    Weak convergence of the sum of dependent variables question

    Hi guys, Problem: Let {Xn},{Yn} - real-valued random variables. {Xn}->{X} - weakly; {Yn}->{Y} weakly. Assume that Xn and Yn - independent for all n and that X and Y - are independent. Show that {Xn+Yn}->{X+Y} weakly. This can be shown using Levy's theorem and characteristic functions...
  19. M

    Position dependent acceleration, one dimension

    I'm just considering motion of a particle along the x-axis, with a given inital position and velocity, and a position dependent acceleration. acceleration = - \frac{1}{x^2} Find the position of the particle after 5 seconds. The particle inital position is -3x, the inital velocity is 3 x/s. So I...
  20. M

    Is this statement about n linearly dependent vectors true?

    Is this statement true or false if false a counterexample is needed if true then an explanation A list of n linearly dependent vectors in an n-dimensional vector space cannot span the space.