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

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    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 10:26 AM. Reason: Name misspelled
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    Last edited by admin; March 26th 2005 at 11:49 AM.
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    Arrow April 9 exercise

    Here is another practice problem:
    http://www.math.ilstu.edu/krzysio/4-9-5-KO-Exercise.pdf
    Yours,
    Krzys'
    Last edited by admin; April 4th 2005 at 08:59 AM.
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    Author, Instuctor and Seminar Provider krzysio's Avatar
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    April 23 exercise

    Some discrete probability basics:
    http://www.math.ilstu.edu/krzysio/4-...O-Exercise.pdf
    Enjoy.
    Yours,
    Krzys'
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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.

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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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