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  • exam P questions

    Hello. I have the following questions.

    1. Let X, Y and Z be three independently and indenticallly distributed continious random variables. Find P(X<=Y<=Z)
    Ans choices: (A) 1/6 (B) 1/5 (c) 1/4 (d) 1/3 (e) 1/2

    2. Let X be a discrete random variable with moment generating function

    M_x(t) = 1/(2-t) + summation(j = 0 ---> infinity) e^(tj-1)/(2j!)

    Note: tj = t multipled by j.

    Ans choices: (A) 1-e^-1 (b) 0.5(1-e^-1) (c) 1/2 + summation (j=0-->infinity)(e^(t*j-1)/2*j! (d) 0.5(1-e^-1+e^-2) (e) 1/2

    3. At a party, 9 people put their hats in the center of a room where the hats are mixed together. Each person then randomly selects one hat. Denote X the number of people who select their own hat. Find Var(X)

    Ans choices: (A) 4 (B) 3 (c) 2 (d) 1 (e) 0.5


    4. Mary pruchases an auto insurance policy fron an insurance company which covers partial damage or total loss of her car for one year period. This policy is subject to a deductible of $1000, and a maximum payment of $10,000. During the policy year the probability o f a partial damage to Mary's car is 0.04 and the prob of total loss of her car is 0.02. If there is partial damage to her car, the amount of damage X follows a distribution with the density function
    f(x) = 1/12500, xbelongs to (0,12500), 0 otherwise

    Ans choices: (A) 408 (B) 410 (c) 424 (d) 450 (e) 550



    For the above questions, I made strong efforts towards obtaining a solution, but I still did not obtain the answer listed in the above choices.

    Any help would be greatly appreciated.

    Thank you.

  • #2
    Ok, since I don't actually see a question in #4, I'm guessing it is something akin to "Find the expected payment by the insurer." We need to break it up into what is paid in a partial loss and what is paid in a total loss. Let X stand for a loss.

    Payment made in partial loss =
    0, x < 100
    x - 1000, 100<x<10000
    10000, x>10000

    You probably already see why this is because 0 will be paid in the presence of a $100 deductible for losses less than $100, and $10000 is the capped payment. Now we must find the expected payment under partial loss over these three regions using the appropriate loss function.

    1st integration: 0

    2nd integration: (x-1000)/12500 -->3240

    For the third region, notice that a constant amount will be paid for losses above 10000. So, we don't need to perform an integration; and thus, the expected payment over this region = 10000(1-F(10000))=2000

    So, under a partial loss, the expected payment is:
    Probability of partial loss occurrence * (0 + 3240 + 2000) = .04 * 5240 =209.6

    Now, for the total loss, we already know that the insurer will pay at most $10000.
    So, under a total loss, the expected payment is:
    Probability of total loss occurrence * 10000 = .02 * 10000 = 200.

    Add these two expected payments --> 200+ 209.6 = 409.6 ~ $410.

    If someone sees something I messed up, please show me. Otherwise, I hope this helps, and God Bless on the studying for the test!

    Also, what is the actual question for #2? I don't know if I will be able to help on that, though . . .
    Last edited by .Godspeed.; June 18 2005, 05:51 PM.
    act justly. walk humbly. .

    Comment


    • #3
      Question #2 on previous post

      sorry, question 2 asks to find P(X>=1)

      Comment


      • #4
        Did that help?
        act justly. walk humbly. .

        Comment


        • #5
          Originally posted by audia4

          3. At a party, 9 people put their hats in the center of a room where the hats are mixed together. Each person then randomly selects one hat. Denote X the number of people who select their own hat. Find Var(X)

          Ans choices: (A) 4 (B) 3 (c) 2 (d) 1 (e) 0.5
          Bump.

          I think Prof. Ostaszewski's 7/16/05 exercise could help with your problem:

          http://www.math.ilstu.edu/krzysio/7-...O-Exercise.pdf
          act justly. walk humbly. .

          Comment


          • #6
            Originally posted by audia4

            1. Let X, Y and Z be three independently and indenticallly distributed continious random variables. Find P(X<=Y<=Z)
            Ans choices: (A) 1/6 (B) 1/5 (c) 1/4 (d) 1/3 (e) 1/2

            2. Let X be a discrete random variable with moment generating function

            M_x(t) = 1/(2-t) + summation(j = 0 ---> infinity) e^(tj-1)/(2j!)

            Note: tj = t multipled by j.

            Ans choices: (A) 1-e^-1 (b) 0.5(1-e^-1) (c) 1/2 + summation (j=0-->infinity)(e^(t*j-1)/2*j! (d) 0.5(1-e^-1+e^-2) (e) 1/2
            Hmmm, #1 and #2 also look extremely similar to Prof. Ostaszewski's 7/2/05 and 7/9/05 practice exercises:

            http://www.math.ilstu.edu/krzysio/7-2-5-KO-Exercise.pdf
            http://www.math.ilstu.edu/krzysio/7-9-5-KO-Exercise.pdf

            audia, are you using study material he wrote?
            act justly. walk humbly. .

            Comment


            • #7
              Your question 1 is already answered

              Dear audia4:

              Your question 1 is already answered in my exercise for July 2, see the sticky
              thread at the top of exam P/1 area in this forum. Look it up.

              Yours,
              Krzys' Ostaszewski

              Originally posted by audia4
              Hello. I have the following questions.

              1. Let X, Y and Z be three independently and indenticallly distributed continious random variables. Find P(X<=Y<=Z)
              Ans choices: (A) 1/6 (B) 1/5 (c) 1/4 (d) 1/3 (e) 1/2

              2. Let X be a discrete random variable with moment generating function

              M_x(t) = 1/(2-t) + summation(j = 0 ---> infinity) e^(tj-1)/(2j!)

              Note: tj = t multipled by j.

              Ans choices: (A) 1-e^-1 (b) 0.5(1-e^-1) (c) 1/2 + summation (j=0-->infinity)(e^(t*j-1)/2*j! (d) 0.5(1-e^-1+e^-2) (e) 1/2

              3. At a party, 9 people put their hats in the center of a room where the hats are mixed together. Each person then randomly selects one hat. Denote X the number of people who select their own hat. Find Var(X)

              Ans choices: (A) 4 (B) 3 (c) 2 (d) 1 (e) 0.5


              4. Mary pruchases an auto insurance policy fron an insurance company which covers partial damage or total loss of her car for one year period. This policy is subject to a deductible of $1000, and a maximum payment of $10,000. During the policy year the probability o f a partial damage to Mary's car is 0.04 and the prob of total loss of her car is 0.02. If there is partial damage to her car, the amount of damage X follows a distribution with the density function
              f(x) = 1/12500, xbelongs to (0,12500), 0 otherwise

              Ans choices: (A) 408 (B) 410 (c) 424 (d) 450 (e) 550



              For the above questions, I made strong efforts towards obtaining a solution, but I still did not obtain the answer listed in the above choices.

              Any help would be greatly appreciated.

              Thank you.
              Want to know how to pass actuarial exams? Go to: smartURL.it/pass

              Comment

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