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Chapter_3__selected - Chapter 03 - Random Variables RANDOM...

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Chapter 03 - Random Variables CHAPTER 3 RANDOM VARIABLES 3.1.a. ) ( P x = 1.0 b. x F( x ) 0 0.3 1 0.5 2 0.7 3 0.8 4 0.9 5 1.0 c. P( X > 2) = 1 - F(2) = 0.3 3.2.a. ) ( P x = 1.0 b. x F( x ) 0 0.01 1 0.10 2 0.40 3 0.60 4 0.80 5 0.90 6 1.00 c. ) 4 ( P X = F(4) = 0.80 d. ) 2 ( P X = 1 - F(1) = 0.90 3.3.a. ) ( P x = 1.0 b. x F( x ) 0 0.10 10 0.30 20 0.65 30 0.85 40 0.95 50 1.00 c. P( X > 20) = 1 - F(20) = 0.35 3-1
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Chapter 03 - Random Variables 3.4.a. ) 4 2 ( P X = 0.2 + 0.2 + 0.3 = 0.7 b. x F( x ) 0 0.1 1 0.2 2 0.4 3 0.6 4 0.9 5 1.0 c. ) ( P x = 1.0 3.5.first die outcome: 1 2 3 4 5 6 1 2 3 Second 4 die out- 5 come: 6 X = sum of the two dice. Note from the sample space that one outcome leads to a sum of 2, two equally- likely outcomes lead to a sum of 3, three lead to a sum of 4, four to a sum of 5, five to a sum of 6, and six (the highest number of outcomes) lead to a sum of 7. Thus, the most likely sum is x = 7. Afterwards, the probabilities decline: five outcomes lead to a sum of 8, four to a sum of 9, three to a sum of 10, two to a sum of 11, and one outcome (two “sixes”) leads to a sum of 12. We thus have the following probability distribution and cumulative distribution function: X P( x ) F( x ) 2 1/36 1/36 3 2/36 3/36 4 3/36 6/36 5 4/36 10/36 6 5/36 15/36 7 6/36 21/36 8 5/36 26/36 9 4/36 30/36 10 3/36 33/36 11 2/36 35/36 12 1/36 1.0 3-2
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Chapter 03 - Random Variables 3-6. a. ) ( P x = 1.0 b. x F( x ) 0 0.1 1 0.3 2 0.7 3 0.8 4 0.9 5 1.00 c. ) 4
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This note was uploaded on 11/24/2010 for the course MATH BAOI taught by Professor Phong during the Spring '10 term at Wash. College.

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Chapter_3__selected - Chapter 03 - Random Variables RANDOM...

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