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

1. ## 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.

6. ## April 9 exercise

Here is another practice problem:
http://www.math.ilstu.edu/krzysio/4-9-5-KO-Exercise.pdf
Yours,
Krzys'

8. ## April 23 exercise

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

9. ## 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. 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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