ps3 - ECE 804, Random Signal Analysis OSU, Autumn 2009...

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

View Full Document Right Arrow Icon
ECE 804, Random Signal Analysis Oct. 12, 2009 OSU, Autumn 2009 Due: Oct. 19, 2009 Problem Set 3 Problem 1 We consider a random selection of coins, where the probability of heads, C for the coins is a random variable whose pdf is f C ( c ) = k · c for 0 c 1 and zero otherwise. (a) Find k . (b) Find P ( H ) for a single coin toss. (c) Let E be the event that we choose a coin, flip it n times, and heads appears k of these times. Find P ( E ). (d) Find the conditional pdf f C | E ( c | E ). (e) Find the probability that heads appears in the ( n + 1)st toss given that k heads has appeared in the first n tosses. Useful fact: R 1 0 x m (1 - x ) n dx = m ! n ! ( m + n +1)! , m,n > 0 Problem 2 Consider a random variable X that is passed through a system that has gain with clipping, defined by y = f ( x ) = g · x, | x | ≤ a ga, x a - ga, x ≤ - a where g and a are given positive constants. (a) Find F Y ( y ) in terms of F X ( x ). Sketch F Y ( y ) for a given generic F X ( x ) (such as a Gaussian CDF). (b) Find
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/30/2009 for the course EE 804 taught by Professor Staff during the Spring '08 term at Ohio State.

Page1 / 3

ps3 - ECE 804, Random Signal Analysis OSU, Autumn 2009...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online