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2007 Exam 3Solutions

# 2007 Exam 3Solutions - IE 111 Fall 2007 Exam 3 Instructions...

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IE 111 SOLUTIONS Fall 2007 Exam 3 Instructions 1. The test is open book, open notes. 2. You must show sufficient work to receive credit. 3. You do not need to interpolate in any tables you use. Just use the closest value. 4. All probabilities should be worked out to a number when possible 5. Each of the 4 problems is worth 25%. 10:00 9:00 30's 30's 1 40's 224 40's 478 50's 478 50's 12456 60's 245567789 60's 23333688 70's 11234557778 70's 1236 80's 2559 80's 23 90's 1 90's 6 Mean 69.1 Mean 63.2 Med 71 Med 63 S 12.5 S 13.8 N 31 N 27

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Question 1 Random variable X has the following probability density function: f(x) = 3 for 0 ≤ x ≤ 0.2 f(x) = k for 0.2 ≤ x ≤ 0.5 f(x) = 0 otherwise a) Find k so that f(x) is a valid pdf. 1 = (3)(0.2)+(k)(0.3) 1 – 0.6 = 0.3k k=0.4/0.3 k = 1.3333 b) Find E(X) 2 . 0 6 84 . 0 06 . 0 6 16 . 0 1 06 . 0 6 ) 04 . 0 )( 4 ( 6 ) 25 . 0 )( 4 ( 0 2 ) 04 . 0 )( 3 ( 6 4 2 3 3 4 3 5 . 0 2 . 0 2 2 . 0 0 2 . 0 0 2 5 . 0 2 . 0 = + = - + = - + - = + = + x x xdx xdx c) Find F(x) for x in the range 0.2 ≤ x ≤ 0.5 5 . 0 2 . 0 for 3 4 1 3 8 . 0
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