hmwk8sol

# hmwk8sol - ISyE 3232 Stochastic Manufacturing and Service...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Fall 2011 H. Ayhan Solutions to Homework 8 1. (a) The state space is { \$10 , \$20 } . The transition matrix is . 8 0 . 2 . 1 0 . 9 . It is irreducible. (b) The state space is { \$10 , \$25 } . The transition matrix is . 9 . 1 . 15 0 . 85 . It is irreducible. (c) The stationary distribution is ( π X \$10 ,π X \$20 ) = (1 / 3 , 2 / 3). (d) The stationary distribution is ( π Y \$10 ,π Y \$25 ) = (3 / 5 , 2 / 5). (e) What you need look at is E ( ∑ 300 i =1 X i ) and E ( ∑ 300 i =1 Y i ). And choose the one with larger expectation. By the stationary distribution obtained in (b) and (c), we have E ( 300 X i =1 X i ) = 300(10 × 1 3 + 20 × 2 3 ) = 5000 , E ( 300 X i =1 Y i ) = 300(10 × 3 5 + 25 × 2 5 ) = 4800 , so you should pick stock 1. 2. First you should solve a few small examples, for instance: . 25 0 . 75 . 75 0 . 25 and . 2 0 . 4 0 . 4 . 3 0 . 3 0 . 4 . 5 0 . 3 0 . 2 In the first case, the stationary distribution is { . 5 , . 5 } , and, in the second case, the sta-...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

hmwk8sol - ISyE 3232 Stochastic Manufacturing and Service...

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

View Full Document
Ask a homework question - tutors are online