# HW4S - ECE 402 Communications Engineering Homework 4...

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

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: ECE 402: Communications Engineering Homework 4 Solutions (Fall 2009) 1. (a) Student GPA X is Gaussian distributed with μ = 3 . 05 and σ = 0 . 50. The probability that a student graduates Summa Cum Laude is then Pr { X ≥ 3 . 75 } = Pr ‰ X- μ σ ≥ 3 . 75- 3 . 05 . 50 = Q (1 . 4) = 0 . 08076 so about 8.1% of students graduate with this honor. (b) The probability of graduating Magna Cum Laude is Pr { 3 . 5 ≤ X < 3 . 75 } = Pr { X ≥ 3 . 5 } - Pr { X ≥ 3 . 75 } = Pr ‰ X- μ σ ≥ 3 . 5- 3 . 05 . 50- Q (1 . 4) = Q (0 . 9)- Q (1 . 4) = 0 . 18406- . 08076 = 0 . 1033 so about 10.3% of students earn this honor. 2. The PSD is the Fourier Transform of the autocorrelation function: P X ( f ) = F { R ( τ ) } = F { A exp(- 2 λ | τ | ) } = 2 A 2 λ [1 + (2 πf/ 2 λ ) 2 ] = λA λ 2 + π 2 f 2 which follows from F{ exp(-| t | /T ) } = 2 T 1+(2 πfT ) 2 for T = 1 / 2 λ . 3. (a) Y ( t ) is filtered white Gaussian noise, so Y ( t ) is a zero-mean Gaussian process with PSD P Y ( f ) =...
View Full Document

## This note was uploaded on 01/28/2012 for the course ECE 402 taught by Professor Townsend during the Fall '08 term at N.C. State.

### Page1 / 3

HW4S - ECE 402 Communications Engineering Homework 4...

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

View Full Document
Ask a homework question - tutors are online