MidtermII_SP06

MidtermII_SP06 - Name_ Stat 427 Rumsey, Goel Midterm 2...

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Name________________________ Stat 427 Midterm 2 Spring, 2006 Rumsey, Goel Remarks: There are five problems for a total of 100 points. The number of points for each problem is given in the parenthesis. You must show full work for credit. Problem 1.(30 points) Let the random variable X denote the length of time (in hours) for which a book on a 2-hour reserve at a library is actually checked out. The density function of X is as follows: 01 ( ) 2 - 12 0. xx f x otherwise ≤≤ = Note: The graph of this function is a triangle with vertices at (0,0), (1,1), and (2,0). a. (8 points) Find the probability that a randomly selected student who checks out this book will return it within an hour? b. (12 points) Given that a student checks out the book out for more than an hour, what is the probability that he/she will keep it for at least 1.5 hour? c. (5 points) Find the median length of time that this book will be checked out. d. (5 points) Find the expected value of the random variable X .
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Name________________________ Problem 2.(30 points) The joint density function of X and Y
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MidtermII_SP06 - Name_ Stat 427 Rumsey, Goel Midterm 2...

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