Test _Supp_ - X . Determine the probability distribution...

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

Engineering Mathematics 4 March 2009 Midterm Test 1 (Supplementary) Name: ID: Answer all two questions. Question 1 a. For each of the functions listed below, state whether or not the func- tions are legitimate probability distributions. Justify your answer. f ( x ) = ( x - 1)( x + 1) , 0 < x < 2 f ( x ) = 1 . 5 x ( x + 1) , - 1 < x < 1 b. The joint probability distribution function of two continuous random variables X and Y is f XY ( x,y ) = xy ( x + 5) for - 1 < x < 1 and 0 < y < c , where c is an unknown constant. Let Z = ( X - 1) 2 be a new random variable obtained via the transforma- tion of the random variable
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X . Determine the probability distribution function of Z . (Hint: You would need to solve for c foremost.) [4+6 marks] Question 2 The state transition matrix of a Markov chain with state space S = { 1 , 2 , 3 } is P =   . 7 0 . 2 0 . 1 . 5 0 . 5 . 8 0 . 2   a. Sketch the state transition diagram. b. Determine the limiting state probability of all three states. c. Show that P (2) 21 = f (2) 21 and interpret this observation. [2+5+3 marks] AT Page 1/1...
View Full Document

This note was uploaded on 08/31/2009 for the course FET eem taught by Professor Alan during the Spring '09 term at Multimedia University, Cyberjaya.

Ask a homework question - tutors are online