hw2 - solutions

hw2 - solutions - IE 336: Operations Research - Stochastic...

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

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IE 336: Operations Research - Stochastic Models Homework Set #2 Solutions Spring 2008 1. (a) Let p = P ( Chip = Good ) = 3 4 , and let q = P ( Chip = Bad ) . Then, q = 1- P ( Chip = Good ) = 1- p = 1- 3 4 = 1 4 (b) Let X = Number of bad chips in group of n X Binomial ( n,p ) Then, P ( X x ) = parenleftbigg n 1 parenrightbigg p (1- p ) n- 1 + parenleftbigg n 2 parenrightbigg p 2 (1- p ) n- 2 + parenleftbigg n 3 parenrightbigg p 3 (1- p ) n- 3 (c) E ( x ) = nq = 1 4 n 2. We need the parameters, a and b, to evaluate the uniform distribution. These can be obtained due to knowledge of the expectation and variance (i.e. via simultaneous equations) So, E ( X ) = a + b 2 = 2 and, V ar ( X ) = ( b- a ) 2 12 = 1 3 . Solving for a and b we obtain a = 1 and b = 3. E [ X n ] = integraltext x x n f ( x ) dx = integraltext b a x n 1 b- a dx = 1 b- a bracketleftBig 1 n +1 x n +1 bracketrightBig b a = 1 b- a bracketleftBig b n +1- a n +1 n +1 bracketrightBig 10 = 1 3- 1 bracketleftBig 3 n +1- 1...
View Full Document

Page1 / 2

hw2 - solutions - IE 336: Operations Research - Stochastic...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online