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Homework0AKey - Spring 2012 STAT 512 HW 0A 1 Homework 0A...

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Unformatted text preview: Spring 2012 STAT 512 HW 0A 1 Homework 0A (Review?) due Jan. 13 The following problem set is based from information in Appendix A. This is review or new material depending on which statistics course you took as a pre-requisite. 1. (From A.3) A certain automobile manufacturer equips a particular model with either a six- cylinder engine or a four-cylinder engine. Let X 1 and X 2 be fuel efficient for independently and randomly selected six-cylinder and four-cylinder cars, respectively. The means and standard deviations are as follows: E{X 1 } = 22 {X 1 } = 1.2 E{X 2 } = 26 {X 2 } = 1.5 a) Calculate the mean and standard deviation of D = X 1 X 2 . E{D} = E{X 1 } E{X 2 } = 22 26 = -4 ? = 2 1 + 2 2 = 1.2 2 + 1.5 2 = 1.921 b) Calculate the mean and standard deviation of T = X 1 + X 2 . E{T} = E{X 1 } + E{X 2 } = 22 + 26 = 48 = 2 1 + 2 2 = 1.2 2 + 1.5 2 = 1.921 = ? c) Calculate the mean and standard deviation of A = T/2. ? = ? { } 2 = 48 2 = 24 = 2 = 1.921 2 = 0.960 2. (A.4) Suppose the tensile strength of type-A steel has a distribution of N( = 105 ksi, 2 = 64 ksi 2 ) and the tensile strength of type-B steel has a distribution of N( = 100 ksi, 2 = 36 ksi 2 ). Assume that the strengths of the two types of steel are independent. Let T = A + B....
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Homework0AKey - Spring 2012 STAT 512 HW 0A 1 Homework 0A...

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