Mathematics for Computer Science

17.4. Great Expectations 593 you guess right? Eric guesses right? no yes no yes 1=2 1=2 1=2 1=2 1=2 1=2 yes 1=2 no 1=2 yes 1=2 n ...

Chapter 17 Random Variables594 To compute your expected return, you use equation (17.2): ExŒpayoffçD 0
1 8 C 1
1 8 C 1
1 8 ...

17.4. Great Expectations 595 you guess right? Eric guesses right? no yes no yes 1=2 1=2 1=2 1=2 1=2 1=2 yes 0 no 1 yes 1 no 0 ye ...

Chapter 17 Random Variables596 scenario, we find that ExŒpayoffçD 0
0 C 1
1 4 C 1
1 4 C 4
0 C.2/
0 C.2/
1 4 C.2/
1 4 ...

17.5. Linearity of Expectation 597 It was as if the players were colluding to lose! If any one of them guessed correctly, then t ...

Chapter 17 Random Variables598 A small extension of this proof, which we leave to the reader, implies Theorem 17.5.2.For random ...

17.5. Linearity of Expectation 599 LettingGbe the number of men that get their own hat, we want to find the expectation ofG. But ...

Chapter 17 Random Variables600 For example,Aicould be the event that theith man gets the right hat back. But in general, it coul ...

17.5. Linearity of Expectation 601 indicator random variable for theith coin coming up heads, that is, JiWWD ( 1 if theith coin ...

Chapter 17 Random Variables602 17.5.4 The Coupon Collector Problem Every time we purchase a kid’s meal at Taco Bell, we are grac ...

17.5. Linearity of Expectation 603 of meals until we get a new kind of car isn=.nk/by the Mean Time to Failure rule. This means ...

Chapter 17 Random Variables604 converges. Then Ex " 1 X iD 0 Ri D X^1 iD 0 ExŒRiç: Proof. LetTWWD P 1 iD 0 Ri. We leave it to t ...

17.5. Linearity of Expectation 605 There is a special case when such a relationshipdoeshold however; namely, when the random var ...

Chapter 17 Random Variables606 The probability thatRDSis the same as the probability thatRtakes whatever valueShappens to have, ...

17.5. Linearity of Expectation 607 for allb 2 V, then the eventsŒRDSçandŒSDTçare independent. This implies that these events are ...

Chapter 17 Random Variables608 because Team 1 has a strategy that guarantees that it wins at least 3/7 of the time, no matter ho ...

17.5. Linearity of Expectation 609 (a)Give the distributions after the 2nd, 3rd, and 4th step by filling in the table of probabi ...

Chapter 17 Random Variables610 (a)Abusystudent must complete 3 problem sets before doing laundry. Each problem set requires 1 da ...

17.5. Linearity of Expectation 611 The single 20 point question is awarded either 12 or 18 points with equal probability.  Le ...

Chapter 17 Random Variables612 If there is a girl in front, behind, to the left, or to the right of a boy, then the two of themf ...