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 Xs be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with M1 = H2 = 20, M3 = M4 = M5 = 24, and oí = oz = 4 for the economy brand and oz = 04 = 0} = 3.5 for the name brand. Define the rv Y by x + X₂ X₃ + X4 + X, 2 so that Y is a measure of the difference in efficiency between economy gas and name-brand gas. 3 Compute Oy.[3 decimal places]

Answer 1

Question 288²= 3.5 0²-62² = 4 ; 63² os Y= X1 + X2 X3+X4 +X5 3 Vas (4) = Vas ( X₂ - Var (x1) + Ivar (X2) + L. vas (X3)+ 5. Vas (X4)+ 5. Var (45) X4 X5 + 2 3 3 4 4 2 so = 9 2.0%+ 4.032+ 1.05+ ou (4+4) + 5 (31573.5+3.5) (10.5) = Ivar (y) 18 70.5 28.5 vas (y) = 2 + = 3.1666667 9 = by 3.) 666667 = l. 779 Answer