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set1 - ECSE-305 Winter 2009 Probability and Random Signals...

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ECSE-305, Winter 2009 Probability and Random Signals I Assignment #1 Posted: Tuesday, Jan. 13, 2009 Due: Tuesday, Jan. 20, 2009, NO later than 2h30pm (please use the assignment box) Student #1: Name: ID: Student #1: Name: ID: Question Marks 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Total

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1. Let A = { 1 , 2 , . . . , 8 , 9 } , B = { 2 , 4 , 6 , 8 } , C = { 1 , 3 , 5 , 7 , 9 } , D = { 3 , 4 , 5 } and E = { 3 , 5 } . Which of the above sets, represented by X , satisfy the given conditions? (a) X and B are disjoint; (b) X D but X * B ; (c) X A but X * C ; (d) X C but X * A . 2. State whether the following sets are finite or infinite sets. If infinite, specify if they are countable or uncountable. (a) A = { all prime numbers } (b) B = { x R : 0 < x < 10 } (c) C = { x Q : 0 < x < 10 } (d) D = { x N : 0 < x < 10 } (e) E = { x N : x 2 = 10 } 3. Show that each of the sets A B and B can be represented as a union of mutually exclusive sets as follows: A B = A ( B - A ) and B = ( A B ) ( A c B ) Illustrate each situation by means of a Venn diagram. 4. Consider the following sequences (i.e. indexed families) of intervals of the real axis, where the index i N : A i = ( - 1 i , 1 i ) , B i = [ - 1 i , 1 i ] , C i = (0 ,
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