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exam2-practice-plustables - 36-225 INTRODUCTION TO...

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36-225 INTRODUCTION TO PROBABILITY & STATISTICS I – Midterm II Practice Exam NOTE: The actual exam will also have some multiple choice questions You must show your work in order to get full or be considered for partial credit. You may use a single sheet of notes (8.5 by 11 inches) and a calculator. You may not share a calculator, pencil, paper or anything else during the exam. Your ANDREW ID: Your First Name: Your Last Name: Your Signature: For Grader use: Problem Total Correct 1 2 3 4 5 6 7 8 9 Total 200 *** Do not turn this page until instructed to do so.*** 1
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Please check that you have pages 2 through 11 + 3 tables . 1. Let the random variable X have the following density function: f X ( x ) = k · x 0 x 1 0 otherwise (a) Find the value of k that will make this a legitimate density function. (b) Obtain F X ( x ) , the cdf of X . (c) Find E ( X ) (d) Find P ( X > . 25 | X < . 75) 2
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2. Assume that X , the time it takes ’student A’ to complete a homework assignment is an exponential random variable with parameter β = 2 hours.
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