Show that if events E and F are independent of each other, then so are E and F′' . [ Hint : Since E ∩ F and E ∩ F ′ are mutually exclusive, we have Pr ( E ) = Pr ( E ∩ F ) + Pr ( E ∩ F ′ ) . ]
Show that if events E and F are independent of each other, then so are E and F′' . [ Hint : Since E ∩ F and E ∩ F ′ are mutually exclusive, we have Pr ( E ) = Pr ( E ∩ F ) + Pr ( E ∩ F ′ ) . ]
Solution Summary: The author explains that the events E and F are independent and the provided expression is mathrmPr(E)=
(4) (8 points)
(a) (2 points) Write down a normal vector n for the plane P given by the equation
x+2y+z+4=0.
(b) (4 points) Find two vectors v, w in the plane P that are not parallel.
(c) (2 points) Using your answers to part (b), write down a parametrization r: R² —
R3 of the plane P.
(2) (8 points) Determine normal vectors for the planes given by the equations x-y+2z = 3
and 2x + z = 3. Then determine a parametrization of the intersection line of the two
planes.
(3) (6 points)
(a) (4 points) Find all vectors u in the yz-plane that have magnitude [u
also are at a 45° angle with the vector j = (0, 1,0).
= 1 and
(b) (2 points) Using the vector u from part (a) that is counterclockwise to j, find an
equation of the plane through (0,0,0) that has u as its normal.
Chapter 6 Solutions
MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications (12th Edition)
Elementary Statistics: Picturing the World (7th Edition)
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