HW1 solution

HW1 solution - Econ 3190 Fall 2010 HW#1 Solution 1 Denote...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 3190 Fall 2010 HW #1 Solution 1. Denote event in (a), (b), (c) and (d) as event E: (a) P ( E ) = P ( A [ B ) = P ( A ) + P ( B ) P ( A \ B ) (b) P ( E ) = P ( A [ B ) P ( A \ B ) = P ( A ) + P ( B ) 2 P ( A \ B ) (c) P ( E ) = P ( A [ B ) = P ( A ) + P ( B ) P ( A \ B ) (d) P ( E ) = 1 P ( A \ B ) (a) A [ ( A c \ B ) = ( A [ A c ) \ ( A [ B ) = S \ ( A [ B ) = ( A [ B ) (b) ( A \ B ) [ ( A c \ B ) = ( A [ A c ) \ B = B 3. (a) Not necessarily. We know A \ B = but can we conclude A c \ B c = as well? We have to consider 2 cases: i. A and B are collectively exhaustive, that is to say A [ B = S: From above, A c \ B c = ( A [ B ) c = S c = As such, if A and B are collectively exhaustive and A and B are mutually exclusive, A c and B c are mutually exclusive as well. ii. A and B are NOT collectively exhaustive, that is to say A [ B ± S: And A c \ B c = ( A [ B ) c 6 = S c = _ . Hence, in this case, A c and B c are NOT mutually exclusive.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

HW1 solution - Econ 3190 Fall 2010 HW#1 Solution 1 Denote...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online