Question

Five automobiles of the same type are to be driven on a 300-mile trip. The first two will use an economy brand of gasoline, and the other three will use a name brand. Let X1, X2, X3, X4, and X; be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with Hi = H2 = 20, 43 = M4 = 15 = 24, and oỉ = og = 4 for the economy brand and oz = o ; = ož = 3.5 for the name brand. Define the ru Y by X1 + X2 X3 + X4 + X5 Y = 2 3 so that Y is a measure of the difference in efficiency between economy gas and name-brand gas.

Answer 1

als which 3 a (X8+Xutxsy het y be a wandom variable as Y = X1 + X₂ measure the difference between economy gas and name-brand gas- in efficiencies Then the expectation of y Taking expectation on both sides El Ef x1+x2] - € [ x3 +Xyttes = z[e(x) +€1x3] - TECxs]+E(Xy) +6CxS -=[ 20420) - To 24+24+24 = 20-24 -4 variance of varly?! Vaul Mp4 Xe )+ Van [X3+xy+ xs] Note that covariance term will vanish since the X, , X2, X₃, Xy, X5 am windepelently die Tributed Vay (4) I. [varl Xi) + Vos ( X2]'+4 [Varcha) +varl Xy)+ Verkko Il 4+4] ++ 35+3.5+3.5) 4 Mova A 4 = 2 + 1.167 = . 167 y will be distributed with mean-4 and variance 3.167. See

Please note that there is no mention of what has been asked in question clearly so the question has been solved based on the what is asked to define.

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