Solution 4.1

# Solution 4.1 - b) 5 . 25 . 25 . ) 5 . 1 ( 5 . 2 5 . 1 2 2 =...

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2. Customers at a fast-food restaurant buy both sandwiches and drinks. The following joint distribution summarizes the numbers of sandwiches (X) and drinks (Y) purchased by customers. X 1 sandwich 2 sandwich 1 drink 0.4 0.2 0.6 Y 2 drink 0.1 0.25 0.35 3 drink 0 0.05 0.05 Total 0.5 0.5 1 X P(X) X P(X) X² P(X) Y P(Y) Y P(Y) Y² P(Y) 1 0.5 0.5 0.5 1 0.6 0.6 0.6 2 0.5 1 2 2 0.35 0.7 1.4 Total 1.5 2.5 3 0.05 0.15 0.45 Total 1.45 2.45 a) Find the expected value and variance of the numbers of sandwiches.
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Unformatted text preview: b) 5 . 25 . 25 . ) 5 . 1 ( 5 . 2 5 . 1 2 2 = = =-= = X X X 59 . 3475 . 3475 . ) 45 . 1 ( 45 . 2 45 . 1 2 2 = = =-= = Y Y Y c) ov(x,y) = xy P XY (x, y) - x y COV(x,y) = (1)(1)(0.4)+(1)(2)(0.2)+(2)(1)(0.1)+(2)(2)(0.25)+(3)(1)(0)+(3)(2)(.05) (1.5) (1.45) = 2.3 2.175 = 0.125 424 . ) 59 . ( 5 . 125 . ) , ( = = = y x y x COV...
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## Solution 4.1 - b) 5 . 25 . 25 . ) 5 . 1 ( 5 . 2 5 . 1 2 2 =...

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