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
Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Problem Set 4 Due October 6, 2010 1. Random variables X and Y have the joint PMF c ( x 2 + y 2 ) , if x { 1 , 2 , 4 } and y { 1 , 3 } , p X,Y ( x, y ) = , otherwise. (a) What is the value of the constant c ? (b) What is P ( Y < X )? (c) What is P ( Y > X )? (d) What is P ( Y = X )? (e) What is P ( Y = 3)? (f) Find the marginal PMFs p X ( x ) and p Y ( y ). (g) Find the expectations E [ X ], E [ Y ] and E [ XY ]. (h) Find the variances var( X ), var( Y ) and var( X + Y ). (i) Let A denote the event X Y . Find E [ X  A ] and var( X  A ). 2. The newest invention of the 6.041/6.431 staff is a threesided die with faces numbered 1, 2, and 3. The PMF for the result of any one roll of this die is p X ( x ) = 1 / 2 , if x = 1 , 1 / 4 , if x = 2 , 1 / 4 , if x = 3 , , otherwise....
View
Full
Document
This note was uploaded on 01/11/2012 for the course EE 6.431 taught by Professor Prof.dimitribertsekas during the Fall '10 term at MIT.
 Fall '10
 Prof.DimitriBertsekas
 Electrical Engineering

Click to edit the document details