Discrete Mathematics for Computer Science

Variance, Standard Deviation, and the Law of Averages 537 from Section 8.7.5, E(XI + X 2 ) = A1 + A2. Applying Theorem l(a) of t ...

(^538) CHAPTER 8 Discrete Probability by Theorem 1. Hence, 1 --n or2 Var(Y) = L Var(Xi) = i=1 Because of their importance, we hi ...

Exercises 539 does not depend on n. Suppose we choose some small positive value for C. No matter what we choose, we can make the ...

540 CHAPTER 8 Discrete Probability Continuation of Exercise 5. Record the average number of heads obtained for each run of 100 ...

Chapter Review 541 the sum of their expectations. We concluded by discussing how likely it is that the average of a set of rando ...

542 CHAPTER 8 Discrete Probability THEOREMS Bayes' Rule Total Probability 8.7 Summary TERMS binomial distribution function binom ...

Chapter Review 543 Flip a fair coin eight times. What is the probability of getting five heads? If the coin is biased and comes ...

544 CHAPTER 8 Discrete Probability Find the probability that at a deal of a hand of bridge, at least one of the four players wi ...

Chapter Review 545 Define the random variable X to be the price of the lot for 601, 02. (07. Find the expected value of X. Let ...

546 CHAPTER 8 Discrete Probability (f) Describe in detail the event E C Q2 that at least one processor at each stage is up, and ...

Chapter Review 547 (e) Note that QŽ is the disjoint union of the events E* and E*. Use this observation and the Theorem of Total ...

548 CHAPTER 8 Discrete Probability A system has four components numbered 1, 2, 3, and 4 as shown: The system performs if eithe ...

Recurrence Relations The analysis of algorithms is an area of interest in computer science, because it directly benefits the wis ...

550 CHAPTER 9 Recurrence Relations In Figure 9.2, examples of legal and illegal moves are shown. The algorithm for solv- ing the ...

The Tower of Hanoi Problem 551 It is instructive to follow the steps of the procedure for an initial configuration in- volving t ...

552 CHAPTER 9 Recurrence Relations 9.1.1 Recurrence Relation for the Tower of Hanoi Problem The complexity of an algorithm is de ...

The Tower of Hanoi Problem 553 = 8T(n - 3) + 4 + 2 + 1 2 = 23 T(n - 3) + Z2' i=0 At this point, we want to look at the results o ...

554 CHAPTER 9 Recurrence Relations Proof Letn 0 =l.LetT={n eN:T(n)=2n-1}. (Base step) First, show that the conclusion holds for ...

Solving First-Order Recurrence Relations 555 In this case, c = 2, f(n) = 1 for all n > 1, and the boundary value is given for ...

556 CHAPTER 9 Recurrence Relations Since T(k) = f(k), replace the reference to T on the right-hand side of the equation, getting ...