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SS08_CSE201_Lecture_03

# SS08_CSE201_Lecture_03 - CSE 201 Lecture 03 Tuesday January...

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1 CSE 201 Lecture 03 Tuesday January 15 , 2008

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2 Notables ± Reminder ² Read Chapters 1, 2, and 3 ± Homework #2 posted, due Thursday ± Forthcoming topics ² Math Review ± Discrete Probability ² System review ² Object representation
3 Exercise ± Compute the following summation: 5 0 21 3 k k = +

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4 Exercise 5 0 2 1 201 211 221 231 241 251 3 333333 12 14 16 18 1 1 0 1 33 3 3 3 3 112334 1 4 k k = + × + ⎡⎤ =+ ++++ ⎢⎥ + ⎡⎤ ⎡ ⎤ ⎡ + + + + = ⎢⎥ ⎢ ⎥ ⎢ =+++++ =
5 Probability Theory ± Random Experiment ² Tossing a coin ² Counting frames through an Ethernet segment ² Calls frequency to Dell’s technical service ² Water level at Cedar River ± Random Variable x : ² A variable whose value depends on the outcome of a random experiment. ± A random variable is either discrete or continuous ± Sample Space S : ² The set of all the outcomes of a random experiment ± Probability of an event E : ² The number of ways that the event E can occur divided by the total number of outcomes

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6 Rolling Two Dice ± Let (die #1, die#2) denote a possible outcome of rolling two dice. Here is a listing of all possible outcomes (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) ± What events can we define here?
7 Example ± What is the probability of rolling 6? ² There are five out of 36 ways to get 6 ² 5/36 ± What is the probability of rolling 7 or 11? ² 8/36 12 11 10 9 8 7 6 11 10 9 8 7 6 5 10 9 8 7 6 5 4 9 8 7 6 5 4 3 8 7 6 5 4 3 2 7 6 5 4 3 2 1 6 5 4 3 2 1 Dice Two-Dice sum event

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8 Expected Value Let be the different values that random variable can take on. be the probability of each value. The expected value of , denoted ( ), is given by ( ) i ii i x x px xE x Ex p x
9 Example ± Let x represent the outcome of our two dice sum event. What is the expected value of x ? 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 Probabilities 12 11 10 9 8 7 6 5 4 3 2 Values x 12 3456 ( ) 234567 36 36 36 36 36 36 54 3 2 1 8 9 10 11 12 7 36 36 36 36 36 ii i Ex p x = × + × + × + × + × + × + ×+ ×=

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10 System Review
11 Main Components ± Hardware ² Physical devices: Processor, memory, keyboard, monitor, mouse, etc. ± Software ² Executable Programs: word processor, spread sheet, internet browser, etc.

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