Solution_Mid2SP07

Solution_Mid2SP07 - NAME: SOLUTION to Midterm II_ STAT 427...

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NAME: SOLUTION to Midterm II_ 1 of 4 pages 5/25/2007 STAT 427 Midterm II Spring, 2007 Prof. Goel MWF 9:30 - 10.20 Problem 1. [10 points] A gas station has two islands: Island #1 has six pumps, and Island #2 has four pumps. Let the random variables X and Y denote: X = number of pumps in use at Island #1, and Y = number of pumps in use at Island #2. a. [2 points] Describe the set of all possible values of ( x,y ) . { ( , ) : {0,1,2,3,4,5,6}, {0,1,2,3,4}} x y xy ∈∈ A total of 7x5 = 35 possible pairs of ( x,y ) values b. [2 points] Give the possible values for T = the total number of pumps in use. T : Possible values: {0,1,2,3,4,5,6,7,8,9,10} c. [2 points] Give the possible values for A D = the absolute difference between the numbers of pumps in use at Islands 1 and 2. AD: Possible values: {0,1,2,3,4,5,6} d. [2 points] Z = the number of islands having exactly two pumps in use. Z : Possible values: {0,1,2} e. [2 points] Explain why X and Y may not be independent random variables. It is unlikely that P [ Y =4| X =0] is equal to P [ Y =4]. Similarly it is unlikely that P [ X =6| Y =0] is equal to P [ X =6]. Hence, the two random variables may not be independently distributed. Problem 2. [20 Points] (i) [8 Points] Twenty-five percent of all telephones of a certain brand are submitted for service while under warranty. Of these, 60% can be repaired whereas the other 40% must be replaced with new units. If a company purchases ten of these
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This note was uploaded on 04/16/2010 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.

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Solution_Mid2SP07 - NAME: SOLUTION to Midterm II_ STAT 427...

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