HW3Solutions - ESI 6321 APPLIED PROBABILITY METHODS FOR...

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Prof. Edwin Romeijn ESI 6321 Applied Probability Methods For Engineers Homework 3 - Solutions Spring 2008 1/4 ESI 6321 APPLIED PROBABILITY METHODS FOR ENGINEERS Homework 3 – Spring 2008 Solutions Exercise 12.1.2 (a) Since x =20, we have β β = + = + - × = 0 1 ( ; ) 123.0 ( 2.16 20) 79.8 E Y x x (b) β Δ = Δ = - × = - 1 2.16 10 21.6 y x (c) ( ) ( ) + - × = 2 2 1 ~ 123.0 ( 2.16 25),4.1 69,4.1 Y N N ( ) ( ) - - = = ≤ - = 1 1 69 60 69 Pr 60 Pr Pr 2.19 0.014 4.1 4.1 Y Y Z (d) ( ) ( ) + - × = 2 2 1 ~ 123.0 ( 2.16 40),4.1 36.6,4.1 Y N N ( ) ( ) - - - = = - = 1 1 36.6 30 36.6 40 36.6 Pr 30 40 Pr 4.1 4.1 4.1 Pr 1.61 0.83 0.743 Y Y Z (e) The distribution of the purity of the solution at catalyst levels x=30 and x=27.5 is, respectively: ( ) ( ) ( ) ( ) + - × = + - × = 2 2 30 2 2 27.5 ~ 123.0 ( 2.16 30),4.1 58.2,4.1 ~ 123.0 ( 2.16 27.5),4.1 63.6,4.1 Y N N Y N N so that their difference is distributed as ( ) ( ) = - - + = - 2 2 2 30 27.5 ~ 58.2 63.6,4.1 4.1 5.4,5.8 D Y Y N N We can thenn determine the desired probability as follows: ( ) ( ) ( ) ( ) = - = - - - - = = = 30 27.5 30 27.5 Pr Pr 0 Pr 0 ( 5.4) 0 ( 5.4) Pr 5.8 5.8 Pr 0.93 0.824 Y Y Y Y D D z
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Prof. Edwin Romeijn ESI 6321 Applied Probability Methods For Engineers Homework 3 - Solutions Spring 2008 2/4 Exercise 12.2.2 First we need to find the values of XX S and XY S : = = = = = = - = - × =  = - = - × × =   ∑ ∑ 2 2 2 1 1 1 1 1 1 1 5.196 8.552 1.539 20 1 1 216.6 8.552 398.2
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  • Spring '07
  • JosephGeunes
  • Statistical hypothesis testing, 1%, 0.2%, 16 degrees, applied probability methods, Prof. Edwin Romeijn

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