
#61




Exercise for December 3, 2005
It is posted at:
http://www.math.ilstu.edu/krzysio/12...OExercise.pdf I hope you will enjoy it. And Merry Christmas, and Happy New Year, and happy holidays to everyone. Yours, Krzys' 
#62




Exercise for December 10, 2005
It is posted at:
http://www.math.ilstu.edu/krzysio/12...OExercise.pdf I hope you will enjoy it. And Merry Christmas, and Happy New Year, and happy holidays to everyone. Yours, Krzys' Ostaszewski author of the ASM manual for Course P 
#63




Exercise for December 17, 2005
It is posted at:
http://www.math.ilstu.edu/krzysio/12...OExercise.pdf I hope you will enjoy it. Merry Christmas, Happy New Year, and happy holidays to everyone. Yours, Krzys' Ostaszewski author of the ASM manual for Course P 
#64




Exercise for December 24, 2005
It is posted at:
http://www.math.ilstu.edu/krzysio/12...OExercise.pdf I hope you will enjoy it. Merry Christmas, Happy New Year, and happy holidays to everyone. Yours, Krzys' Ostaszewski author of the ASM manual for Course P 
#65




Exercise for December 31, 2005
It is posted at:
http://www.math.ilstu.edu/krzysio/12...OExercise.pdf I hope you will enjoy it. Happy New Year! Yours, Krzys' Ostaszewski author of the ASM manual for Course P 
#66




In the Nov. 1981 Course 110 Exam Problem No. 34
Why couldn't we use the limits for x as 0<x<1/2?? I somehow got the right answer for the joint density but didn't use the limits of 1/2y to 1/2 for x. I used 0<x<1/2!! When i compared my result. I knew it was wrong but couldn't figure what else to do. Dr. Krzys could you kindly help me out...thanks! 
#67




You only integrate over values where the density is positive. E.g., suppose you are considering the marginal density of y = .7. You don't want to include the point (.1, .7) since that is not within the shaded part of his diagram. The lowest value of x that has any density when y = .7 is x = .35.

#68




Thank you, Gandalf
Quote:
Yours, Krzys' 
#69




Thanks to you both! It's just that I always see it when there is the solution posted but am not able to discern for myself easily. Any tips as to how to determine limits??

#70




Drawing the picture is usually a big help. Then if the region is not a rectangle, the limits are going to require care. Recognizing the enemy is the first step in winning the battle.
Maybe krzysio will have some specific suggestions. 
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