265%20F07%20MT1

# 265%20F07%20MT1 - IOE 265 Fall 2007 1st Exam(80 minute exam...

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1 IOE 265 Fall 2007 1 st Exam (80 minute exam) October 8, 2007 Part I. Multiple choice questions BCDBD Part II. True/False Problems TFTFT Part III. Fill in Blanks 0.205; 0.40; 0.951; k=12/25; () 4 4 0 . 4 0 . 6 xx PX x x ⎛⎞ == ⎜⎟ ⎝⎠ or b(x; 4, 0.4) or binomial (n=4; p=0.4) Part IV. Short Questions 1. A customer visiting the suit department of a certain store will purchase: A suit with probability 0.22 A shirt with probability 0.30 A tie with probability 0.28 Both a suit and a shirt with probability 0.11 Both a suit and a tie with probability 0.14 Both a shirt and a tie with probability 0.10 All three items with probability 0.06 What is the probability that a customer purchase none of the items? Solution: A: suit B: shirt C: tie [] (' ' ' )1 ( ) 1 ( ) ( ) ( )( ) 1 0.22 0.30 0.28 0.11 0.14 0.10 0.06 1 0.51 0.49 PA B C PAPBPC PA B PA C PB C =− + = ++−−−+ = ∩∩ ∪∪ ∩∩∩∩ 2. Assume X is a continuous random variable with the following density function:

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2 3 1 00 45 0 1 1 x x X xx ex < =≤ < a. Obtain and sketch the cumulative distribution function.
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265%20F07%20MT1 - IOE 265 Fall 2007 1st Exam(80 minute exam...

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