2assignment

# 2assignment - Assignment 2 Problems 1 Illustrate the effect...

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: Assignment 2 Problems: 1. Illustrate the effect of undersampling x ( t ) = cos(2 πf t ) for a sampling rate of f s = 3 2 f . 2. Let X be a non-negative discrete r.v. with pmf Pr( X = i ) = p i (for i = 0 , 1 ,... ) and cdf (for x = 0 , 1 ,... ) F X ( x ) defines Pr( X ≤ x ) = x summationdisplay i =0 p i Let Y be a non-negative continuous r.v. with pdf f Y ( y ) and cdf F Y ( y ). (a) Show that E [ X ] = ∑ i ≥ p i i can also be computed in terms of the cdf with E [ X ] = ∞ summationdisplay i =0 (1- F X ( i- 1)) . Hint: Count how many times each p i appears in the standard E [ X ]. (b) Show that E [ Y ] = integraltext ∞ f Y ( y ) y dy can also be computed in terms of the cdf with E [ Y ] = integraldisplay ∞ (1- F Y ( y )) dy. 3. Using a biased coin to make an unbiased decision. Alice and Bob want to choose between the opera and the movies by tossing a fair coin. Unfortunately, the only available coin is biased and lands heads with probability p . Since they both know p , whomever calls the...
View Full Document

## This note was uploaded on 11/13/2011 for the course ECEN 455 taught by Professor Staff during the Spring '08 term at Texas A&M.

### Page1 / 2

2assignment - Assignment 2 Problems 1 Illustrate the effect...

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

View Full Document
Ask a homework question - tutors are online