HW9-2 - R and pdf f N ( n ) = 1 2 e- | n | for a positive...

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

ECE 302, Homework #9. Due date: 3/30 http://www.ece.purdue.edu/ chihw/ECE302 07.html Prof. Chih-Chun Wang Email: chihw@purdue.edu Oﬃce: MSEE354 Oﬃce Hours: MWF: 12pm–1pm TA: Kamesh Krishnamurthy, Email: kkrishna@purdue.edu Oﬃce: POTR 370 Oﬃce Hours: M: 10–11am TTh: 10:30am–12:30pm Question 1: Select three events from Problem 4.1(a) to 4.1(i) by yourself, and sketch their corresponding regions on the two dimensional plane R 2 . Question 2: Problem 4.4. Question 3: Problem 4.9(a), 4.9(b). Find the marginal cdf of X . How do you derive the marginal pdf of X from the marginal pdf of X ? Problem 4.9(c). Question 4: Problem 4.11. Question 5: Problem 4.12(c) Question 6: Problem 4.17. Do not be afraid by the “Laplacian random variable,” which is simply a random variable with sample space being

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R and pdf f N ( n ) = 1 2 e- | n | for a positive constant > 0. For 4.17(c), you are asked to compute P ( X = 1 | Y > 0) and P ( X =-1 | Y > 0). Question 7: Problem 4.38(ac). Hints: 1. For 4.38(a), We notice that Y = N + x is just another Gaussian with mean x and variance 2 N . 2. For 4.38(c), since f X,Y ( x,y ) = f X | Y ( x | y ) f Y ( y ), the conditional f X | Y ( x | y ) is the ratio of the joint pdf f X,Y ( x,y ) divided by the marginal pdf f Y ( y ). So your goal is to nd f Y ( y ). You can use the following formula to nd f Y ( y ): f Y ( y ) = Z x =- f X,Y ( x,y ) dx (1) [Optional] Ask yourself why f Y ( y ) can be obtained from the above integral....
View Full Document

This note was uploaded on 05/02/2009 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue University-West Lafayette.

Page1 / 2

HW9-2 - R and pdf f N ( n ) = 1 2 e- | n | for a positive...

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

View Full Document
Ask a homework question - tutors are online