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Thread: Weekly Practice Exam "P" Problems courtesy of Dr Krzysztof Ostaszewski

  1. #1

    Arrow Weekly Practice Exam "P" Problems courtesy of Dr Krzysztof Ostaszewski

    Thank you Dr. Krzysztof Ostaszewski for suggesting we post some of your sample problems. . Watch for further exam problems as he makes them available to us.
    Last edited by krzysio; August 4th 2005 at 11:26 AM. Reason: Name misspelled
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  2. #2

    Arrow March 12th Problem

    [url="http://www.math.ilstu.edu/krzysio/3-12-5-KO-Exercise.pdf"]http://www.math.ilstu.edu/krzysio/3-12-5-KO-Exercise.pdf[/url]
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  3. #3

    Arrow March 19th Problem

    [url="http://www.math.ilstu.edu/krzysio/3-19-5-KO-Exercise.pdf"]http://www.math.ilstu.edu/krzysio/3-19-5-KO-Exercise.pdf[/url]
    Last edited by admin; March 26th 2005 at 12:49 PM.
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  4. #4

    Arrow March 26th Problem

    [url="http://www.math.ilstu.edu/krzysio/3-26-5-KO-Exercise.pdf"]http://www.math.ilstu.edu/krzysio/3-26-5-KO-Exercise.pdf[/url]
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  5. #5

    Arrow April 2nd Problem

    [url="http://www.math.ilstu.edu/krzysio/4-2-5-KO-Exercise.pdf"]http://www.math.ilstu.edu/krzysio/4-2-5-KO-Exercise.pdf[/url]
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  6. #6
    Author, Instuctor and Seminar Provider krzysio's Avatar
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    Arrow April 9 exercise

    Here is another practice problem:
    [url="http://www.math.ilstu.edu/krzysio/4-9-5-KO-Exercise.pdf"]http://www.math.ilstu.edu/krzysio/4-9-5-KO-Exercise.pdf[/url]
    Yours,
    Krzys'
    Last edited by admin; April 4th 2005 at 09:59 AM.
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  7. #7
    Author, Instuctor and Seminar Provider krzysio's Avatar
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    April 16 exercise

    [url]http://www.math.ilstu.edu/krzysio/4-16-5-KO-Exercise.pdf[/url]
    Enjoy,
    Krzys'
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  8. #8
    Author, Instuctor and Seminar Provider krzysio's Avatar
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    April 23 exercise

    Some discrete probability basics:
    [url]http://www.math.ilstu.edu/krzysio/4-23-5-KO-Exercise.pdf[/url]
    Enjoy.
    Yours,
    Krzys'
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  9. #9
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    question about the 3-19-5 problem

    I have a question about the 3-19-5 problem posted. In the 4th line of the solution:

    Cov(X1-aX2-bX3,X2) = Cov(X2,X1) - aVar(X2) - bCov(X3,X2)

    I'm not sure how you got from left hand side to the right hand side of the equation. I've never seen an covariance example like this. I'm familiar with the equation for the covariance of 2 variables, but not of the variance of an expression and a variable. Could you generalize the rule for me? Thanks very much.

  10. #10
    Actuary.com - Level VI Poster
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    Quote Originally Posted by engelbmj
    I have a question about the 3-19-5 problem posted. In the 4th line of the solution:

    Cov(X1-aX2-bX3,X2) = Cov(X2,X1) - aVar(X2) - bCov(X3,X2)

    I'm not sure how you got from left hand side to the right hand side of the equation. I've never seen an covariance example like this. I'm familiar with the equation for the covariance of 2 variables, but not of the variance of an expression and a variable. Could you generalize the rule for me? Thanks very much.
    I think you can think of covariance like an inner product, or, if you like, the FOIL method. So, in this case,
    Cov(x1 - ax2 - bx3, x2)
    = Cov(x1,x2) - Cov(ax2,x2) - Cov(bx3,x2)
    = Cov(x1, x2) - a*Cov(x2,x2) - b*Cov(x3, x2)
    = Cov(x1, x2) - a*Var(x2) - b*Cov(x3, x2)

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