Homework_8 - in the 3rd edition). 3. Papoulis 6-48 (6-18 in...

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ECE600 Random Variables and Waveforms Mark R. Bell Spring 20 1 1 MSEE 336 Homework Assignment #8 Should be completed by Session 2 4 . Reading Assignment: Read Sections 6-4 through 6-7 of Papoulis. 1. Papoulis 6-40 (6-14 in 3rd edition). 2. Papoulis The random variables X and Y are Gaussian, independent, and have iden- tical variance σ 2 . Show that if Z = p X 2 + Y 2 , then f Z ( z )= z σ 2 I 0 σ 2 ¥ e ( z 2 + η 2 ) / 2 σ 2 , where η = p η 2 X + η 2 Y , and I 0 ( x ) is the modified Bessel function of order zero: I 0 ( x )= 1 2 π Z 2 π 0 e x cos θ dθ. Hint: See Example 6-16 on pages 191–192 of Papoulis (or the development page 140
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Unformatted text preview: in the 3rd edition). 3. Papoulis 6-48 (6-18 in 3rd edition). 4. Papoulis 6-49 (7-1 in 3rd edition). 5. Papoulis 6-50 (7-2 in 3rd edition). 6. Papoulis 6-51 (7-3 in 3rd edition). 7. Papoulis 6-52 (7-4 in 3rd edition). 8. Papoulis 6-54 (7-7 in 3rd edition). 9. Papoulis 6-71 (7-10 in 3rd edition). 10. Papoulis 6-74 (7-11 in 3rd edition). 11. Papoulis 6-77 (7-14 in 3rd edition). 1...
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This note was uploaded on 10/12/2011 for the course ECE 600 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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