wi2008.finalsolutions

# wi2008.finalsolutions - CSE 21 Winter 2008 Final Exam...

This preview shows pages 1–3. 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: CSE 21 Winter 2008 Final Exam Solutions Roy Liu University of California at San Diego 1 a By guessing that g ( n ) = αr n 1 + βr n 2 , we get 0 = r 2- 5 r + 6 r ∈ { 2 , 3 } . Applying initial conditions, we get that g (0) = 0 = α + β g (1) = 1 = α · 2 + β · 3 α =- 1 β = 1 g ( n ) =- 2 n + 3 n . b By guessing that g ( n ) = αr n + βnr n , we get 0 = r 2- 4 r + 4 r = 2 . Applying initial conditions, we get that g (0) = 0 = α g (1) = 1 = α · 2 + β · 2 α = 0 β = 1 / 2 g ( n ) = n 2 n- 1 . 2 Let D be the random variable counting the number of defective light bulbs chosen. We have E [ D ] = 3 summationdisplay i =0 i * Pr [ D = i ] = 0 * parenleftbigg 4 parenrightbiggparenleftbigg 6 3 parenrightbiggslashbiggparenleftbigg 10 3 parenrightbigg + 1 * parenleftbigg 4 1 parenrightbiggparenleftbigg 6 2 parenrightbiggslashbiggparenleftbigg 10 3 parenrightbigg + 2 * parenleftbigg 4 2 parenrightbiggparenleftbigg 6 1 parenrightbiggslashbiggparenleftbigg 10 3 parenrightbigg + 3 * parenleftbigg 4 3 parenrightbiggparenleftbigg 6 parenrightbiggslashbiggparenleftbigg 10 3 parenrightbigg ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

wi2008.finalsolutions - CSE 21 Winter 2008 Final Exam...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online