{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw5 - λe-λx and λe-λy respectively Let Z = X Y Find the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 351K Probability, Statistics, and Random Processes SPRING 2009 Instructor: Shakkottai/Vishwanath { shakkott,sriram } @ece.utexas.edu Homework 5 (Due 03/09/2009) Problem 1 Consider two continuous random variables Y and Z and a random variable X that is equal to Y with probability p and to Z with prbability 1 - p . Show that the PDF of X is given by f X ( x ) = pf Y ( x ) + (1 - p ) f Z ( x ) Problem 2 The random variable X has the PDF f X ( x ) = cx - 2 , 1 x 4 0 , otherwise 1. Determine the value of c . 2. Let A be the event { X > 2 } . Calculate P ( A ) and the conditional PDF of X given that event A has occured. Problem 3 Let X and
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: λe-λx and λe-λy respectively. Let Z = X + Y . Find the conditonal PDF of X given Z = z . Problem 4 Let X and Y be two random variables that are independent and uniformly distributed over the interval [0 , 1] . Find the CDF and PDF of | X-Y | . Problem 5 Find c and the PDF of the continuous random variable X associated with the moment generating function M X ( s ) = c. 3 3-s + 3 4 . 7 7-s ....
View Full Document

{[ snackBarMessage ]}