ST
Homework1

# Homework1 - ST561 Fall 2010 Homework 1 Due Monday Oct 4th...

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ST561 Fall 2010 Homework 1 Due: Monday, Oct. 4th, 2010 Note: The first 4 exercises below are not to be handed in. Please make sure you can do them (and ask about them if you have questions). 1. Find the union A 1 S A 2 and intersection A 1 T A 2 of two sets A 1 and A 2 where (a) A 1 = { x : x = 1 , 2 , 3 } , A 2 = { x : x = 2 , 3 , 4 } (b) A 1 = { x : 0 < x < 1 } , A 2 = { x : 1 x < 3 } (c) A 1 = { ( x, y ) : 0 < x < 3 , 0 < y < 3 } , A 2 = { ( x, y ) : 1 < x < 4 , 1 < y < 4 } . 2. Find S k =1 A k if (a) A k = { x : 1 /k x < 2 - 1 /k } , k = 1 , 2 , 3 , . . . (b) A k = { ( x, y ) : 1 /k < x 2 + y 2 4 - 1 /k } , k = 1 , 2 , 3 , . . . 3. Find T k =1 A k if (a) A k = { x : 2 - 1 /k < x 2 } , k = 1 , 2 , 3 , . . . (b) A k = { x : 3 < x 3 + 1 /k } , k = 1 , 2 , 3 , . . . (c) A k = { ( x, y ) : 0 x 2 + y 2 < 1 /k } , k = 1 , 2 , 3 , . . . 4. Textbook P52, 1.3.5(iv). 5. Textbook P52, 1.3.6. 6. A man and a woman (unrelated) each have two children. At least one of the man’s children is a boy, and the woman’s younger child is a boy. Do the chances that the man has two boys equal the chances that the woman has two boys? 7. The following procedure was used in a survey of cheating on taxes. A taxpayer is selected at random among all Oregon taxpayers to be a subject in the survey.

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• 20%, Oregon tax return, Oregon taxpayers, union A1 A2

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