{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

09hw12

# 09hw12 - EE 464 Mitra Homework 12 Due FRIDAY 10am Spring...

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

EE 464, Mitra Spring 2009 Homework 12 Due FRIDAY, April 24, 2009, 10am This problem set investigates random sequences: convergence of random sequences and limit theorems. 1. L-G 7.21. 2. L-G 7.45 (Hint: use the Cauchy-Schwarz inequality). 3. Let ω U [0 , 1] . In what senses do the following sequences converge, it at all? For each sequence, identify the limit and show whether they converge in distribution, in probability, in mean-square, almost surely or surely . (a) X n = sin ( ω + 1 n ) (b) X n = cos n ( ω ) 4. We have a sequence of independent random variables, whose probability density functions for each n are given by f X n ( x ) = 1 - 1 n 1 2 πσ exp " - 1 2 σ 2 x - n - 1 n σ 2 # + 1 n σ exp( - σx ) u ( x ) where u ( x ) is the unit step-function. Determine whether or not the sequence converges in (i) mean-square (ii) probability or (iii) distribution. 5. Consider an i.i.d. sequence of uniform random variables: X n U [0 , 1] . Define the random sequence Y n = min 1 i n X i .

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.

{[ snackBarMessage ]}

### Page1 / 2

09hw12 - EE 464 Mitra Homework 12 Due FRIDAY 10am Spring...

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

View Full Document
Ask a homework question - tutors are online