Homework1key

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 01/29/2014 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue.

Ask a homework question - tutors are online