Discrete Mathematics for Computer Science

Cross Product Sample Spaces 497 Table 8.1 Link Status Sample Spaces Sample Space Link Probability Density Function 021 AB pl(^0 ...

498 CHAPTER 8 Discrete Probability The probability P(E) of E is P(E) = p(to) WEE = (0.9)(0.8)(0.5) + (0.9)(0.8)(0.5) + (0.9)(0.2 ...

Cross Product Sample Spaces 499 Example 3. Consider an n-trial Bernoulli process where each trial has a probability of success p ...

500 CHAPTER 8 Discrete Probability Theorem 2. (Probability of k Successes in a Bernoulli Process) The function p(wk) = b(n; k, p ...

Cross Product Sample Spaces 501 (Inductive step) Suppose that the statement is true for n = k. Now, prove that it is true for n ...

502 CHAPTER 8 Discrete Probability On the other hand, P (E1) = Ell (3)= and P(E 2 ) (Di E 21 = (26) = Hence, 1 P(EI) • P(E 2 ) - ...

Cross Product Sample Spaces 503 However, this event E 2 is part of a larger context in which a coin is flipped. In the grand exp ...

504 CHAPTER 8 Discrete Probability Proof. The event E tl n E i2 n ... n E* 1kof the cross product sample space consists of all n ...

Exercises 505 W Exercises Suppose S is a set with k elements. How many elements are in S', the cross product Sx S x ... x S of ...

506 CHAPTER 8 Discrete Probability A coin that is twice as likely to show heads than it is tails is tossed three times. (a) Des ...

Independent Events and Conditional Probability 507 Suppose the sex of a newborn child is viewed as an experiment with two equal ...

CHAPTER 8 Discrete Probability By Corollaries 1 and 2 of Theorem 3 in Section 8.3.4, pairs of events of the form E and E for i A ...

Independent Events and Conditional Probability 509 Solution. The sample space is Ž = {l, 2, 3, 4, 5, 61. P(A) = P(B) =1/2, but P ...

510 CHAPTER 8 Discrete Probability one another in the following sense. Imagine that we can buy a chance on winning a prize if th ...

Independent Events and Conditional Probability 511 simply divide the original densities for outcomes in A by P (A). (Checking th ...

512 CHAPTER 8 Discrete Probability In other words, the probability of B is not affected by the fact that A has occurred. In fact ...

Independent Events and Conditional Probability 513 Example 4. There are three kinds of vending machines in canteens at the unive ...

514 CHAPTER 8 Discrete Probability One key feature of Bayes' Rule is that it can be used in situations where the underlying prob ...

Independent Events and Conditional Probability 515 Send 0 with 0.8 probability 0.4 o Receive^0 0.2 0.1 Send 1 with -09 l Receive ...

516 CHAPTER 8 Discrete Probability Solution. Each outcome (o = (i, j) c Q can be regarded as an event {o0} g 2, and the Theorem ...