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lec0330 - CS 173 Discrete Mathematical Structures Cinda...

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CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Siebel Center, rm 2213 Office Hours: BY APPOINTMENT

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Cs173 - Spring 2004 CS 173 Announcements Homework 9 available. Due 04/ 02, 8a. Exam 2, Apr 4, 7-9p, Loomis 141. Email Cinda with conflicts. Today’s lecture covers material from Rosen, sections 5.2-5.3.
Cs173 - Spring 2004 CS 173 Birthdays How many people have to be in a room to assure that the probability that at least two of them have the same birthday is greater than 1/ 2? a) 23 b) 183 c) 365 d) 730 Let p n be the probability that no people share a birthday among n people in a room. We want the smallest n so that 1 - p n > 1/ 2. Then 1 - p n is the probability that 2 or more share a birthday.

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Cs173 - Spring 2004 CS 173 A Special Random Variable A Binomial random variable X is a random variable that counts the number of successes in a sequence of n independent Bernoulli trials, where the probability of success on each trial is p. What are the possible values for X? 1, 2, …n We want Pr(X = k), k = 1,…n. From last time, Pr(X = k) = C(n, k) p k (1-p) n-k
Cs173 - Spring 2004 CS 173 A Special Random Variable Suppose a network consisting of 10 computers crashes completely if there are not at least 8 functioning machines. Further, suppose that each machine functions with probability 0.9, independently of the others. What is the probability the network is available?

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