# sol12 - U.C Berkeley — CS70 Discrete Mathematics and...

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: U.C. Berkeley — CS70: Discrete Mathematics and Probability Problem Set 12 Lecturers: Umesh Vazirani & Christos H. Papadimitriou Due November 29, 2006 at 4:00pm Problem Set 12 Solutions 1. Total Annihilation [10 points] Each missile hits each silo with equal probability 1 2620 . Hence T i , the number of trials to destroy the i th missile once ( i- 1)th have been destroyed, has geometric distribution with success probability n − i +1 n for n = 2620. Hence, the expected total number of trials is: E [ T ] = E [ n summationdisplay i =1 ] = n summationdisplay i =1 n n- i + 1 = = n summationdisplay j =1 n j ≈ n log n = 2620log 2620 = 20622 Notice this is exactly the coupon collector problem discussed in class. 2. Significance Levels [10 points] a) m = 70 + 8 + 10 + 13 + 14 + 16 + 17 + 26 8 = 83 v = 13 2 + 5 2 + 3 2 + 0 + 1 2 + 3 2 + 4 2 + 13 2 7 ≈ 56 . 86 Hence, the estimate for the standard deviation is √ v ≈ 7 . 54....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

sol12 - U.C Berkeley — CS70 Discrete Mathematics and...

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

View Full Document
Ask a homework question - tutors are online