ECE 503 – Homework 5 1. Let be as shown below. Find a) :
b) :
c) :
d) :
1 1 2 2 2. Let ∈ 0,1/2 and 2cos 2
a) √2 b) √2 Now let ∈ 0,1 . c) Find all such that √2 d) Why is part c) not asked as “Find e) Find all such that √2 3. Let ∈ 2, 1,0,1 and let a) Find 4 0 b) Find c) Find all such that 1 d) Why is part c) not asked as “Find 4. Let 0,2 , a) 0.25 b) 0.25 c) ∈ 0.09,0.25 . Find √2 ”? . 1 ”? and /2, d) 0.25 e) 0.25 f) ∈ 0.09,0.25 5. Repeat question 4) but with 1,2 . Find the following events: 1,2,3,4,5,6 , 6. Let 2 , and Find the following events: a) 10 d) b) 5 e) c) 5 f) 0
/2
0
7. Let 8. Let ~
9. Let ~
10. Let ~
,
3
0 3
2
10
where 10 3 0 2 0
0
3
2 and let 3
where 3. Find and sketch . 2
and let where 1,2 and let where
2,2 and let . Find . 2
1. Find . where is as shown below. Find and sketch . 1
11. Let 1
2 and let where
Find and sketch . 12. Let ~
/
/
0,1 and let 0 where 0. Show that ~gamma , 1/2 . That is, show .