HWsolution_2 - Univ. Of Maryland at College Park, ECE...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Univ. Of Maryland at College Park, ECE Department ENEE324 Fall 2002 Solution to Assignment #: 2 Posted on: 9/16/02 Problem 1) [GAR] 2.25 a) We had ) ( ) ( ] [ B P A P B A P + U So ) ( ) ( ) ( ) ( ) ( ] ) [( ) ( C P B P A P C P B A P C B A P C B A P + + + = U U U U U Solution 2. using Corollary 7. [ ] ( ) ( ) ( ) ( )( ) ( ) ( ) () Therefor it is enough to prove that ( ) ( ) But so ( ) ( ) Clearly this is true for all three probabiliti PABC P A P B P C PA B PAC P CB P AB C P ABC A B PAB =++ + ---+ ≤++ ⊂≤ U U III II I IIII I I I I es and since these probabilities are non-negative, the statement is true. b) We use induction for 2 = n ) ( ) ( ) ( 2 1 2 1 A P A P A A P + U Let’s assume it is true for k n = i.e. ) ( 1 1 = = k i i k i i A P A P U We will prove it for 1 + = k n or ) ( 1 1 1 1 + = + = k i i k i i A P A P U ( 29 ( 29 ( 29 ( 29 1 1 1 11 1 2 k kk i i k i k i ki b y theassumption ii i o f induction sets PAP A A P A P A P A + + + ++ == =   = + +=     ∑∑ 1442443 U U UU Problem 2: [GAR] 2.31 } 2 / 1 | | ) , {( f y x y x A - = 2 / 1 2 / 1 | | - - - p f y x y x or 2 / 1 f y x - So we draw two lines 2 / 1 & 2 / 1 = - - = - y x y x So 4 / 1 2 / 1 2 / 1 2 / 1 2 / 1 2 / 1 2 / 1 1 ) ( ) ( ) ( 2 1 = × × + × × = + = A Area A Area A P
Background image of page 1

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

View Full DocumentRight Arrow Icon
Problem 3: [GAR] 2.50 P[ AB C] P[ A ( B C) ] P[A ( B C)] P( B C ) P[A ( B C)] P[B C] P[C] ˙˙ = ˙ ˙= / ˙ ˙ = ˙ Problem 4) Take } 5 , 4 , 3 , 2 , 1 , 0 { = A a) } 5 , , , / ) , , {( = + + = z y x A z A y A x z y x S
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

HWsolution_2 - Univ. Of Maryland at College Park, ECE...

This preview shows document pages 1 - 3. Sign up to view the full document.

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