Chapter 1 Covariance

Discussion in 'CS2' started by Aisha, Mar 13, 2019.

  1. Aisha

    Aisha Very Active Member

    Hello
    I'm unable to recall the formula used here for calculating the covariance . This is the solution of Question 1.2(i) from chapter 1 practice questions ( on page 29)
     

    Attached Files:

  2. Calm

    Calm Ton up Member

    These are the covariance formulae used in NTU's CT6 and CT4, respectively.[​IMG]
     
    Last edited: Mar 14, 2019
  3. Aisha

    Aisha Very Active Member

    Hey
    Can you please explain how have we used these formulas in solving the above problem?
     
  4. Calm

    Calm Ton up Member

    [​IMG]
     
    Aisha likes this.
  5. Aisha

    Aisha Very Active Member

    Thanks!
     
  6. Bill SD

    Bill SD Very Active Member

    Thanks Calm and Aisha.
    A related question: The solution for Q1.7 uses the fact that (0,t) and (t,t+s) are non-overlapping time periods. But why does this justify why Cov((X(t), X(t+s)-X(t)) =0?
    Surely this should be broken down to Cov(X(t),-X(t)) +Cov(X(t),X(t+s)). And the first expression Cov(X(t),-X(t)) = var (X(t)) so the solution to the question should be 2var (X(t)) Tia
     
  7. Andrew Martin

    Andrew Martin ActEd Tutor Staff Member

    Hello

    The process has independent increments, so the increment \( X_{t+s} - X_{t} \) is independent of \( { X_u, 0 \le u \le t } \). This means that \( X_{t+s} - X_{t} \) is independent of \( X_t \) and so \(cov(X_{t+s}- X_{t}, X_t ) \) is 0.

    Hope this helps

    Andy
     

Share This Page