Free Weekly Exam questions

[krzysio]

It is posted at:
http://www.math.ilstu.edu/krzysio/12...O-Exercise.pdf
I hope you will enjoy it. And Merry Christmas, and Happy New Year, and happy holidays to everyone.

Yours,
Krzys'

[krzysio]

It is posted at:
http://www.math.ilstu.edu/krzysio/12...O-Exercise.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

[krzysio]

It is posted at:
http://www.math.ilstu.edu/krzysio/12...O-Exercise.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

[krzysio]

It is posted at:
http://www.math.ilstu.edu/krzysio/12...O-Exercise.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

[krzysio]

It is posted at:
http://www.math.ilstu.edu/krzysio/12...O-Exercise.pdf
I hope you will enjoy it. Happy New Year!

Yours,
Krzys' Ostaszewski
author of the ASM manual for Course P

[Dee]

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!

[Gandalf]

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.

[krzysio]

Originally Posted by Gandalf

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.

Thank you, Gandalf. You are quite right. The graph in the solution has the area for which the density is positive marked with dotted lines, and this is the area over which we need to take integrals to calculate probabilities.

Yours,
Krzys'

[Dee]

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??

[Gandalf]

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.