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Chapter 11 - Page 17/18 - normal approx to recursive formula

Discussion in 'SP8' started by krishdear, Mar 16, 2019.

  1. krishdear

    krishdear Member

    In the solution to this question, var(S) has been computed to 30 but if I am using the formula from core reading, I am getting 50, i.e., 10 x 2 + 10 x 3 as E(N) is 10 and var(X) is 2. What am I missing here? Pls help
     
    krishdear, Mar 16, 2019
    #1
  2. Hemant Rupani

    Hemant Rupani Senior Member

    Looks like you are using E(X^2), where it should be [E(X)]^2.

    Actual answer is...
    Var(S)=E(N)*Var(X)+Var(N)*[E(X)]^2
    =10*2+10*1^2=30
     
    Hemant Rupani, Mar 17, 2019
    #2
  3. krishdear

    krishdear Member

    Thanks Hemant - that was very helpful.
     
    krishdear, Mar 18, 2019
    #3
  4. Darren Michaels

    Darren Michaels ActEd Tutor Staff Member

    I have amended the title of this post to refer to the 2019 Course Materials as it looks like you were referring to an old version.

    Don't forget for a compound Poisson you also have the formulae on page 16 of the Tables.

    Hence Var (S) = 10 E(X^2)=10 (var(S)+(EX)^2)=10(2+1)=30.
     
    Darren Michaels, Mar 19, 2019
    #4

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