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Graph 02 015 01 005 0 0 5 10 3 verification 1 fx

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Unformatted text preview: erify that f(x) specifies a legitimate distribution. graph: 0.2 0.15 0.1 0.05 0 0 5 10 3 verification 1) f(x) 0 for all x 2) There are two ways of doing this a) from the graph, this is a triangle, area of the triangle = ½ (base) (height) = ½ (10) (0.2) = 1 b) using integrals Note: You can also do part b) using triangles and symmetry. b) In the long run, what proportion of your total daily waiting times will be at most 3 min? triangle: width = 3, height = f(3) = (0.04)(3) = 0.012; area = ½ (3)(0.12) = 0.18 At least 7 min? triangle: by symmetry, this is the same as at most 3 min, area = 0.13 At least 4 min? triangle: we know that the area under the curve between 5 and 10 is 0.5 area between 4 and 5 = 0.5 – area between 0 and 4 = 0.5 – ½ (4)(0.04)(4) = 0.5 – 0.32 = 0.18 therefore, the total area – 0.5 + 0.18 = 0.68 Between 4 min and 7 min? Triangle: This is the...
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This note was uploaded on 01/29/2014 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue.

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