Homework 5

# Homework 5 - drawn by ﬁrst choosing its distance D from...

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

FALL 2011 Instructor: Sujay Sanghavi [email protected] Homework 5 Due: October 13th in class Problem 1 Let Y be a random variable with probability density function (PDF) f Y ( y ) = 1 + y, - 1 y 0 , y, 0 < y 1 , 0 , otherwise . Find (a) P ( | Y | < 0 . 5) . (b) P ( Y > 0 | Y < 0 . 5) . (c) E [ Y ] . Problem 2 The random variable X has the PDF f X ( x ) = { cx - 2 , 1 x 2 0 , otherwise (a) Determine the value of c . (b) Find the CDF of X . (c) Let A be the event { X > 1 . 5 } . Calculate P ( A ) and the conditional PDF of X given that event A has occurred. Problem 3 Let X be a random variable with PDF f X ( x ) = ± 2 x/ 5 if 2 < x 3 , 0 otherwise . and let f ( X ) = X 2 . Calculate E [ f ( X )] and Var [ f ( X )] . Problem 4 A circle has radius r . Any chord of the circle is at distance at most r from the center. A random chord is

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: drawn by ﬁrst choosing its distance D from the center uniformly from the interval [0 ,r ] , and then choosing any chord at that distance from the center. Find the PDF of L , the length of the chord. Draw a ﬁgure to illustrate. Problem 5 Let the random variables X and Y be jointly uniformly distributed over the region shown. (a) Determine the value of f X,Y on the region shown. (b) Find f X , the mean and variance of X . (c) Find and sketch E [ Y | X = x ] as a function of x . Be sure to specify which range of x this conditional expectation is well deﬁned for....
View Full Document

## This note was uploaded on 02/20/2012 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas.

### Page1 / 2

Homework 5 - drawn by ﬁrst choosing its distance D from...

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

View Full Document
Ask a homework question - tutors are online