Assignment X2

Discussion in 'CS1' started by ykai, Mar 11, 2023.

  1. ykai

    ykai Ton up Member

    1.Q8-(ii)
    Can the constant of all discrete MLEs be obtained in this way?

    2.Q9-(iii)-a
    I don’t understand where the number 9 comes from, and whether there is a contradiction between the above P(Y<=9)=0.005 and the following P(Y>=9)=0.005? I don’t understand the answer here.
     
    ykai, Mar 11, 2023
    #1
  2. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    Hi Ykai
    1. The constant is terms not involving the parameter of interest, it maybe a combination term for discrete data but you may have to think about the particular observations you have been given and the probability of observing the sample when formulating the likelihood.
    2. Do you mean Q12iii ?
    9 is the total number of claims from the sample of 10 policies
    This is the exact confidence interval for lambda, see Ch9 Section 4 Confidence Intervals for binomial and Poisson Parameters, p17
    Hope this helps, thanks Andrea
     
    Last edited: Mar 13, 2023
    Andrea Goude, Mar 13, 2023
    #2
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  3. ykai

    ykai Ton up Member

    1.
    So why do we do this in this question?
    The 50 variables in this question are from the exponential distribution, but why can we get constant this way?

    2.I have found out the blind spot. Thank you!
     
    Last edited: Mar 13, 2023
    ykai, Mar 13, 2023
    #3
  4. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    I have edited my response to make it clearer

    1. We have discrete events, 50 observations, and we can use the exponential distribution to calculate the probabilities of the observations being within those ranges, but they can occur in a variety of orders so that is where the constant term is coming from
     
    Andrea Goude, Mar 13, 2023
    #4
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  5. ykai

    ykai Ton up Member

    So the constant obtained by this method is only approximate and not precise, right?
     
    ykai, Mar 13, 2023
    #5
  6. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    You can work out the constant precisely by considering the combination term, but as we don't need it, as it would be lost when we differentiate, we write this as a constant
     
    Andrea Goude, Mar 13, 2023
    #6
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  7. ykai

    ykai Ton up Member

    Thank you ,I have understood!
     
    ykai, Mar 13, 2023
    #7
  8. CHUN LEONG LEE

    CHUN LEONG LEE Keen member

    Quick qn on Question 2.14x

    Average claim size = 680, and the solution is treating it as Lamda = 680. Would like some clarity on why Lamda = 680 when the expectation is 1/ Lamda (I am viewing that average claim size = mean)

    Thank you.
     
    CHUN LEONG LEE, Apr 8, 2023
    #8
  9. CHUN LEONG LEE

    CHUN LEONG LEE Keen member

    Ps (could not edit the last sentence in time)

    I am viewing that the average claim size of 680 refers to the expected value E(X) = U

    Thank you.
     
    CHUN LEONG LEE, Apr 8, 2023
    #9
  10. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    Xbar is 680, that is used in the question, which as you say is the mean, which is 1/lambda
    I don't see the lambda=680 you mentioned in the solution?
     
    Andrea Goude, Apr 11, 2023
    #10
  11. CHUN LEONG LEE

    CHUN LEONG LEE Keen member

    Apologies, i could not edit my first question

    So in this case when they say the average size = 680, they are referring to E[X] = u = 1/lamda, and not lamda? Just want to confirm my understanding here
     
    CHUN LEONG LEE, Apr 11, 2023
    #11
  12. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    Yes E[X] = mu = 1/lambda
     
    Andrea Goude, Apr 12, 2023
    #12

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